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.

A294502 Binomial transform of A026007.

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%I A294502 #15 Apr 22 2019 07:05:28
%S A294502 1,2,5,15,45,132,381,1086,3060,8531,23563,64560,175639,474790,1275929,
%T A294502 3410180,9068075,23998671,63230680,165904474,433596795,1129037237,
%U A294502 2929620046,7576584801,19532878559,50205938903,128676829149,328895341731,838453003422
%N A294502 Binomial transform of A026007.
%H A294502 Vaclav Kotesovec, <a href="/A294502/b294502.txt">Table of n, a(n) for n = 0..2960</a>
%F A294502 a(n) = Sum_{k=0..n} binomial(n,k) * A026007(k).
%F A294502 a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4 + (3*Zeta(3))^(2/3) * n^(1/3) / 8 - Zeta(3)/16) * Zeta(3)^(1/6) * 2^(n - 1/12) / (3^(1/3) * sqrt(Pi) * n^(2/3)).
%F A294502 G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^k/(1 - x)^k)^k. - _Ilya Gutkovskiy_, Aug 19 2018
%t A294502 nmax = 40; s = CoefficientList[Series[Product[(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 A294502 Cf. A026007, A218481, A294500, A294503, A294504.
%K A294502 nonn
%O A294502 0,2
%A A294502 _Vaclav Kotesovec_, Nov 01 2017