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.

A294530 Binomial transform of A023871.

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%I A294530 #8 Aug 20 2018 07:51:38
%S A294530 1,2,8,33,131,497,1834,6635,23622,82942,287656,986552,3349165,
%T A294530 11263951,37558235,124240204,407951848,1330340478,4310385956,
%U A294530 13881618570,44451643311,141578435571,448634389388,1414774796929,4441038400458,13879652908322,43197263002063
%N A294530 Binomial transform of A023871.
%H A294530 Vaclav Kotesovec, <a href="/A294530/b294530.txt">Table of n, a(n) for n = 0..2600</a>
%F A294530 a(n) = Sum_{k=0..n} binomial(n,k) * A023871(k).
%F A294530 a(n) ~ exp(2^(5/4) * 3^(-5/4) * 5^(-1/4) * Pi * n^(3/4) + Pi^2 * sqrt(n) / (4*sqrt(30)) - Pi^3 * n^(1/4) / (32 * 2^(1/4) * 15^(3/4)) + Pi^4/3840 - Zeta(3)/(4*Pi^2)) * 2^(n - 7/8) / (15^(1/8) * n^(5/8)).
%F A294530 G.f.: (1/(1 - x))*exp(Sum_{k>=1} sigma_3(k)*x^k/(k*(1 - x)^k)). - _Ilya Gutkovskiy_, Aug 20 2018
%t A294530 nmax = 40; s = CoefficientList[Series[Product[1/(1 - x^k)^(k^2), {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]
%Y A294530 Cf. A023871, A218481, A266232, A294500, A294529.
%K A294530 nonn
%O A294530 0,2
%A A294530 _Vaclav Kotesovec_, Nov 02 2017