This site is supported by donations to The OEIS Foundation.

User talk:Peter Bala

From OeisWiki
Jump to: navigation, search


    I'm interested in your addition to A036969, on the central factorial numbers.  Specifically, 

what's the source for your comment that they're the connection coefficients in the expansion x^n = \prod T(n,k) (x-k^2)? This is quite correct, I'm just trying to source it. It's different from the Riordan expansion.

Thanks, William Keith P.S. You can reply at if it's more convenient. And, of course, you can delete this note once you've read it. It's your page.  :^) William J. Keith 19:30, 31 January 2012 (UTC)

Peter, I just wanted to say I'm honored to have my work referenced in your paper at . It makes me feel that it wasn't a complete waste of time :) Drop me a line some-time..

Couple questions

Hi Peter,

Re your "pink comment" in A060294, particularly - "It is one of Ramanujan's - see Zudilin arXiv: 0712.1332v2 equation (1.3) for a reference." Does Zudilin's list the formula in that paper of his in generalized form, formulated by Paul Hanna that is as 2/Pi = Sum_{n>0} (-1)^n * (4*n+1) * Product_{k=1..n} (2*k-1)^3/(2*k)^3. which BTW in Maple format is 2/Pi = sum((-1)^n * (4*n+1) * product((2*k-1)^3/(2*k)^3,k=1..n),n=0...infinity) or does it list it the way Earls put it (with Paul Hanna's correction of course) that is as 2/Pi = 1 - 5*(1/2)^3 + 9*((1*3)/(2*4))^3 - 13*((1*3*5)/(2*4*6))^3 ... ?

By now (after approval) the formula section still misses generalized form

2/Pi = Sum_{n>=0} (-1)^n * (4*n+1) * Product_{k=1..n} (2*k-1)^3/(2*k)^3.

Paul only noted it in the pink section

I think that someone should add it there still - with appropriate attribution - could you do that ?

Also since we are on Pi formula subject - I have another question to ask. Does Zudilin's paper list both a) and b) (or one - then which ?) versions of 24/Pi formulas referenced in A132714, A220852 and in A220853 as:

a) 24/Pi = sum(k>=0, (30*k+7)*C(2*k,k)^2*(Hypergeometric2F1[1/2 - k/2, -k/2, 1, 64])/(-256)^k ). or in Maple style format sum((30*k+7) * binom(2k,k)^2 * (Hypergeometric2F1[1/2 - k/2, -k/2, 1,64])/(-256)^k, k=0...infinity)

Another version of this identity is: b) 24/Pi = sum_{k>=0} ((30*k+7) * binomial(2k,k)^2 * (sum_{m=0,k/2} (binomial(k-m,m) * binomial(k,m) * 16^m))/(-256)^k)

or in Mathematica style format 24/Pi = Sum[(30*k+7) * Binomial[2k,k]^2 * (Sum[Binomial[k-m,m] * Binomial[k,m] * 16^m, {m,0,k/2}])/(256)^k, {k,0,infinity}].


Cheers, Alexander R. Povolotsky 22:14, 24 March 2013 (UTC)

Maple code in A008287

Hi Peter

In Sep 07 2013 you added a formula T(n,k) = sum... and a corresponding Maple program to compute r-nomials.

We recently discovered the same nice formula and spent some time in a quite short proof, but we didn't find any papers containing this formula. Your notice on this site is the only one we have seen so far. Do you have a reference to a corresponding paper? It seems to us that several communities (gray-codes, integer compositions, ...) are not aware that there exists such a simple formula.

Christoph Christoph Stamm 12:35, 11 June 2014 (UTC)