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 A304785 #5 Feb 16 2025 08:33:54
%S A304785 1,-1,-2,-1,-2,4,0,15,7,17,22,26,-79,-2,-12,-392,-250,-392,-443,-640,
%T A304785 -404,-795,5106,1147,3304,4542,32330,21001,23372,21015,14496,16165,
%U A304785 -17213,51296,-231330,-890169,-492310,-755449,-1648273,131600,-6308274,-2160440,-4410945,1593319
%N A304785 Expansion of Product_{k>=1} (1 - p(k)*x^k), where p(k) = number of partitions of k (A000041).
%C A304785 Convolution inverse of A063834.
%H A304785 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%H A304785 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A304785 G.f.: Product_{k>=1} (1 - A000041(k)*x^k).
%t A304785 nmax = 43; CoefficientList[Series[Product[(1 - PartitionsP[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A304785 a[n_] := a[n] = If[n == 0, 1, Sum[-Sum[d PartitionsP[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 43}]
%Y A304785 Cf. A000041, A063834, A271619, A300508.
%K A304785 sign
%O A304785 0,3
%A A304785 _Ilya Gutkovskiy_, May 18 2018