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 A335812 #7 Jun 26 2020 06:22:36
%S A335812 1,-1,3,-7,39,-31,1623,9953,182199,2116289,32269143,505278113,
%T A335812 9743069559,214428606209,5156280298263,127321200213473,
%U A335812 3176128419544119,80737907621585729,2147513299611040983,61423058495936864033,1912348969322283717879,64216042408215934910849
%N A335812 E.g.f.: Product_{k>=1} 1 / (1 - (1 - exp(x))^k).
%C A335812 Inverse binomial transform of A327601.
%F A335812 a(n) = Sum_{k=0..n} (-1)^k * Stirling2(n,k) * k! * A000041(k).
%t A335812 nmax = 21; CoefficientList[Series[ Product[1/(1 - (1 - Exp[x])^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A335812 Table[Sum[(-1)^k StirlingS2[n, k] k! PartitionsP[k], {k, 0, n}], {n, 0, 21}]
%o A335812 (PARI) a(n) = sum(k=0, n, (-1)^k * stirling(n,k,2) * k! * numbpart(k)); \\ _Michel Marcus_, Jun 25 2020
%Y A335812 Cf. A000041, A167137, A327601, A335813.
%K A335812 sign
%O A335812 0,3
%A A335812 _Ilya Gutkovskiy_, Jun 25 2020