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 A306042 #9 Feb 16 2025 08:33:54
%S A306042 1,1,3,8,50,94,2446,-9024,297216,-3183264,64191984,-1041792192,
%T A306042 22098943632,-478805234064,11856288460272,-308662348027008,
%U A306042 8575865689645440,-248582819381690880,7556655091130023680,-240521346554744194560,8049494171497089265920,-283469026458500121634560
%N A306042 Expansion of e.g.f. Product_{k>=1} 1/(1 - log(1 + x)^k).
%H A306042 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A306042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F A306042 E.g.f.: exp(Sum_{k>=1} sigma(k)*log(1 + x)^k/k).
%F A306042 a(n) = Sum_{k=0..n} Stirling1(n,k)*A000041(k)*k!.
%p A306042 a:=series(mul(1/(1-log(1+x)^k),k=1..100),x=0,22): seq(n!*coeff(a,x,n),n=0..21); # _Paolo P. Lava_, Mar 26 2019
%t A306042 nmax = 21; CoefficientList[Series[Product[1/(1 - Log[1 + x]^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A306042 nmax = 21; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] Log[1 + x]^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A306042 Table[Sum[StirlingS1[n, k] PartitionsP[k] k!, {k, 0, n}], {n, 0, 21}]
%Y A306042 Cf. A000041, A006252, A053529, A167137, A320349.
%K A306042 sign
%O A306042 0,3
%A A306042 _Ilya Gutkovskiy_, Jun 17 2018