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 A035297 #18 Jul 08 2025 21:32:06
%S A035297 1,1,2,4,7,12,19,29,43,63,90,127,176,241,327,439,585,773,1015,1322,
%T A035297 1714,2208,2831,3610,4585,5794,7297,9149,11433,14233,17665,21846,
%U A035297 26943,33123,40614,49656,60565,73671,89414,108254,130785,157649,189654,227671,272802,326236,389446
%N A035297 Expansion of sum ( q^n / product( 1-q^k, k=1..5*n), n=0..inf ).
%H A035297 Vaclav Kotesovec, <a href="/A035297/b035297.txt">Table of n, a(n) for n = 0..5000</a>
%F A035297 a(n) ~ Gamma(1/5) * exp(Pi*sqrt(2*n/3)) / (5 * 2^(8/5) * 3^(1/10) * Pi^(4/5) * n^(3/5)). - _Vaclav Kotesovec_, Jun 17 2025
%t A035297 nmax = 50; CoefficientList[Series[Sum[x^k/Product[1 - x^j, {j, 1, 5*k}], {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2025 *)
%t A035297 nmax = 50; p=1; s=1; Do[p=Expand[p*(1-x^(5*k))*(1-x^(5*k-1))*(1-x^(5*k-2))*(1-x^(5*k-3))*(1-x^(5*k-4))];p=Take[p, Min[nmax+1, Exponent[p, x]+1, Length[p]]];s+=x^k/p;, {k, 1, nmax}]; CoefficientList[Series[s, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2025 *)
%Y A035297 Cf. A363068, A385069.
%K A035297 nonn
%O A035297 0,3
%A A035297 _N. J. A. Sloane_
%E A035297 More terms from _Vaclav Kotesovec_, Jun 16 2025