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 A304784 #5 Feb 16 2025 08:33:54
%S A304784 1,-1,-1,-2,0,-1,2,3,11,8,19,13,22,-5,-10,-80,-105,-246,-303,-502,
%T A304784 -506,-681,-400,-231,873,1956,4733,7536,12891,17609,25188,29508,34890,
%U A304784 29690,19039,-17742,-74002,-183563,-333665,-572271,-866683,-1271429,-1698491,-2181207
%N A304784 Expansion of Product_{k>=1} 1/(1 + x^k)^p(k), where p(k) = number of partitions of k (A000041).
%C A304784 Convolution inverse of A261049.
%H A304784 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%H A304784 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A304784 G.f.: Product_{k>=1} 1/(1 + x^k)^A000041(k).
%t A304784 nmax = 43; CoefficientList[Series[Product[1/(1 + x^k)^PartitionsP[k], {k, 1, nmax}], {x, 0, nmax}], x]
%t A304784 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) d PartitionsP[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 43}]
%Y A304784 Cf. A000041, A001970, A089254, A261049, A300508.
%K A304784 sign
%O A304784 0,4
%A A304784 _Ilya Gutkovskiy_, May 18 2018