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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

I do not know that. But, why would you need to?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

I would like a closed form if possible for that series.

Mind if I ask why you came to this page in the OEIS?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I looked at his probabilities and compared them to mine, and I saw that they were always almost the same, except for a factor. So I calculated the first few factors and found that they matched that sequence on OEIS. Why?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Okay, I was just wondering.

I can get a somewhat closed form for T[5,n] but it is ugly and too complicated you will have to go with the series or the gf.

I will test your 4 conjecture now by simulation.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

I think it will be easier to extract the coefficient from the GF.

Tell me when you finish the simulations.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

Hi;

I got 11.216568 for 1 million, this is very close to your answer. What do you get for 5?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Hi bobbym

15.38578772717056256240736291835039673851, or

in closed form.Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

I am getting 15.387028 for 1 million, that is again very close. Your answer for 2?

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I believe it is;

which matches for n=2,3,4,5

Perhaps we can extract a closed form for that..

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

3.774691358024691358024691358024691358025, which agrees with the dice pdf.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi;

You got 1223 / 324 for 2 ?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Yes!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

What do you want to do with your solution?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

I do not know? Can we send it to that guy?

I have found the formula for general number of wanted appearences (not just for 2, 3, 4 and 5):

`f(k):=sum(i*(i-k)!/(6^(i-1))*binomial(i-1,k-1)*coeff(ratexpand((sum(x^j/j!,j,0,k-1))^5),x^(i-k)),i,k,6*k-5);`

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hi gAr;

I did not see you up there, watch out becuase our latex is damaged and does not display plus signs.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Didn't see his post either. Looks like gAr and I got the same formula.

*Last edited by anonimnystefy (2013-02-16 06:37:04)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

Hi;

Yes, I can send it or you can send it. Of course it would be with your name on it. Your final form looks like gAr's.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Hi bobbym

You can send it, but before sending it, please send it to me (in a PM or right here).

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy and bobbym,

Yes, the final form is the same. I was thinking about egfs and anonimnystefy had a form already. So I started working from there. Maybe we can try for a closed form for some time.

It's late here, see you after a few hours.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

Hi;

I think you should post it first right under where I talk about it in the other thread. That will establish the date.

How will we get latex to him in an email?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Hi gAr

Maybe you guys can get an asymptotic form if all else fails...

See you later!

Hi bobbym

Which thread?

*Last edited by anonimnystefy (2013-02-16 06:49:07)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

Hi gAr;

See you later. Have a good night.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Hi bobbym

Which thread?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,791

http://www.mathisfunforum.com/viewtopic.php?id=18866

Be thorough. I will lock the thread after you are done. I am going to take a little break now see you then.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,604

Thorough? About what?

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