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 A304630 #8 Feb 16 2025 08:33:54
%S A304630 1,2,4,6,10,15,22,31,44,60,82,109,145,189,246,316,405,513,648,811,
%T A304630 1013,1256,1553,1908,2339,2852,3469,4200,5074,6105,7330,8769,10470,
%U A304630 12461,14802,17533,20730,24447,28780,33802,39636,46377,54180,63171,73546,85469,99185,114908,132946,153574,177177
%N A304630 Expansion of (1/(1 - x))*Product_{k>=1} (1 - x^(3*k))/(1 - x^k).
%C A304630 Partial sums of A000726.
%H A304630 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionb.html">Partition Function b_k</a>
%H A304630 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A304630 G.f.: (1/(1 - x))*Product_{k>=0} 1/((1 - x^(3*k+1))*(1 - x^(3*k+2))).
%F A304630 G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^k + x^(2*k)).
%F A304630 a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*Pi*n^(1/4)). - _Vaclav Kotesovec_, May 18 2018
%t A304630 nmax = 50; CoefficientList[Series[1/(1 - x) Product[(1 - x^(3 k))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A304630 nmax = 50; CoefficientList[Series[1/(1 - x) Product[1/((1 - x^(3 k + 1)) (1 - x^(3 k + 2))), {k, 0, nmax}], {x, 0, nmax}], x]
%t A304630 nmax = 50; CoefficientList[Series[1/(1 - x) Product[(1 + x^k + x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A304630 Cf. A000070, A000726, A036469, A117276, A304632.
%K A304630 nonn
%O A304630 0,2
%A A304630 _Ilya Gutkovskiy_, May 15 2018