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.
%I A319455 #14 Jan 04 2024 18:09:48
%S A319455 1,2,7,14,35,66,140,252,485,840,1512,2534,4347,7084,11705,18622,29862,
%T A319455 46522,72779,111310,170534,256586,386101,572488,848050,1240974,
%U A319455 1812979,2621486,3782669,5410360,7720237,10932740,15443120,21669546,30327570,42196022,58555543,80832850
%N A319455 Expansion of Product_{k>=1} 1/((1 - x^k)*(1 - x^(2*k)))^2.
%C A319455 Convolution inverse of A002171.
%C A319455 Self-convolution of A002513.
%C A319455 Convolution of A000041 and A029862.
%C A319455 Euler transform of period 2 sequence [2, 4, ...].
%H A319455 Andrew Howroyd, <a href="/A319455/b319455.txt">Table of n, a(n) for n = 0..1000</a>
%F A319455 G.f.: Product_{k>=1} (1 + x^k)^2/(1 - x^(2*k))^4.
%F A319455 G.f.: exp(2*Sum_{k>=1} (4*sigma(k) - sigma(2*k))*x^k/k).
%F A319455 a(n) ~ exp(Pi*sqrt(2*n)) / (2^(13/4)*n^(7/4)). - _Vaclav Kotesovec_, Sep 14 2021
%p A319455 a:=series(mul(1/((1-x^k)*(1-x^(2*k)))^2,k=1..55),x=0,38): seq(coeff(a,x,n),n=0..37); # _Paolo P. Lava_, Apr 02 2019
%t A319455 nmax = 37; CoefficientList[Series[Product[1/((1 - x^k)*(1 - x^(2*k)))^2, {k, 1, nmax}], {x, 0, nmax}], x]
%t A319455 nmax = 37; CoefficientList[Series[1/(QPochhammer[x] QPochhammer[x^2])^2, {x, 0, nmax}], x]
%t A319455 nmax = 37; CoefficientList[Series[Exp[2 Sum[(4 DivisorSigma[1, k] - DivisorSigma[1, 2 k]) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]
%o A319455 (PARI) seq(n)={Vec(exp(2*sum(k=1, n, (4*sigma(k) - sigma(2*k))*x^k/k) + O(x*x^n)))} \\ _Andrew Howroyd_, Sep 19 2018
%Y A319455 Cf. A000041, A001934, A001936, A002171, A002513, A029862.
%K A319455 nonn
%O A319455 0,2
%A A319455 _Ilya Gutkovskiy_, Sep 19 2018