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.

A307264 Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).

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%I A307264 #9 Apr 03 2019 09:04:27
%S A307264 1,2,3,5,10,22,49,107,229,486,1035,2225,4825,10508,22875,49624,107154,
%T A307264 230356,493471,1054602,2250850,4801825,10244940,21865466,46680201,
%U A307264 99659713,212697816,453634533,966551216,2057052465,4372660927,9284272791,19692591418
%N A307264 Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).
%C A307264 Binomial transform of A000700.
%F A307264 G.f.: (1/(1 - x)) * Product_{k>=1} (1 + x^(2*k-1)/(1 - x)^(2*k-1)).
%F A307264 a(n) = Sum_{k=0..n} binomial(n,k)*A000700(k).
%F A307264 a(n) ~ 2^(n-1) * exp(Pi*sqrt(n/3)/2 + Pi^2/96) / (3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2019
%p A307264 a:=series((1/(1-x))*mul(1/(1+(-x)^k/(1-x)^k),k=1..100),x=0,33): seq(coeff(a,x,n),n=0..32); # _Paolo P. Lava_, Apr 03 2019
%t A307264 nmax = 32; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A307264 Cf. A000700, A218481, A266232.
%K A307264 nonn
%O A307264 0,2
%A A307264 _Ilya Gutkovskiy_, Apr 01 2019