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 A035298 #19 Jul 08 2025 21:32:12
%S A035298 1,1,2,4,7,12,19,30,44,65,93,132,183,253,343,462,616,816,1071,1399,
%T A035298 1813,2339,2999,3828,4861,6149,7743,9714,12140,15120,18766,23220,
%U A035298 28640,35224,43199,52838,64458,78441,95226,115336,139381,168077,202258,242900,291140,348300,415922
%N A035298 Expansion of sum ( q^n / product( 1-q^k, k=1..6*n), n=0..inf ).
%C A035298 In general, for m>=1, if g.f. = Sum_{k>=0} x^k / Product_{j=1..m*k} (1 - x^j), then a(n) ~ Gamma(1/m) * exp(Pi*sqrt(2*n/3)) / (m * 2^((3*m + 1)/(2*m)) * 3^(1/(2*m)) * Pi^(1 - 1/m) * n^((m+1)/(2*m))). - _Vaclav Kotesovec_, Jun 17 2025
%H A035298 Vaclav Kotesovec, <a href="/A035298/b035298.txt">Table of n, a(n) for n = 0..5000</a>
%F A035298 a(n) ~ Gamma(1/6) * exp(Pi*sqrt(2*n/3)) / (2^(31/12) * 3^(13/12) * Pi^(5/6) * n^(7/12)). - _Vaclav Kotesovec_, Jun 17 2025
%t A035298 nmax = 50; CoefficientList[Series[Sum[x^k/Product[1 - x^j, {j, 1, 6*k}], {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 16 2025 *)
%t A035298 nmax = 50; p=1; s=1; Do[p=Expand[p*(1-x^(6*k))*(1-x^(6*k-1))*(1-x^(6*k-2))*(1-x^(6*k-3))*(1-x^(6*k-4))*(1-x^(6*k-5))];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 A035298 Cf. A363068, A385070.
%K A035298 nonn
%O A035298 0,3
%A A035298 _N. J. A. Sloane_
%E A035298 More terms from _Vaclav Kotesovec_, Jun 16 2025