cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A294504 Binomial transform of A156616.

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%I A294504 #16 Apr 22 2019 07:05:42
%S A294504 1,3,11,41,147,509,1717,5671,18395,58735,184961,575337,1769981,
%T A294504 5390997,16270587,48696299,144620059,426428645,1249007767,3635595953,
%U A294504 10520770265,30278391475,86689798089,246988386691,700439171501,1977660342139,5560497703461
%N A294504 Binomial transform of A156616.
%H A294504 Vaclav Kotesovec, <a href="/A294504/b294504.txt">Table of n, a(n) for n = 0..2840</a>
%F A294504 a(n) = Sum_{k=0..n} binomial(n,k) * A156616(k).
%F A294504 a(n) ~ exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / 4 + (7*Zeta(3))^(2/3) * n^(1/3) / 8 + 1/12 - 7*Zeta(3)/48) * (7*Zeta(3))^(7/36) * 2^(n - 1/12) / (A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
%F A294504 G.f.: (1/(1 - x))*exp(Sum_{k>=1} (sigma_2(2*k) - sigma_2(k))*x^k/(2*k*(1 - x)^k)). - _Ilya Gutkovskiy_, Oct 15 2018
%t A294504 nmax = 40; s = CoefficientList[Series[Product[((1+x^k)/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]
%Y A294504 Cf. A156616, A218481, A294500, A294502, A294505.
%K A294504 nonn
%O A294504 0,2
%A A294504 _Vaclav Kotesovec_, Nov 01 2017