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 A317280 #20 Nov 19 2023 08:22:02
%S A317280 1,2,4,10,30,108,444,2112,11040,65712,414816,2992944,21876816,
%T A317280 188936928,1527813216,15991733376,133364903040,1794144752640,
%U A317280 13329036288000,270750383400960,1167153128110080,57074973648030720,-103080839984916480,17319631144046423040,-171982551742151685120
%N A317280 Expansion of e.g.f. 1/(1 - log(1 + x))^2.
%C A317280 Exponential self-convolution of A006252.
%H A317280 Seiichi Manyama, <a href="/A317280/b317280.txt">Table of n, a(n) for n = 0..451</a>
%H A317280 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A317280 a(n) = Sum_{k=0..n} Stirling1(n,k)*(k + 1)!.
%F A317280 a(n) ~ n! * 2 * (-1)^(n+1) / (n * log(n)^3) * (1 - 3*(gamma+1) / log(n) + (6*gamma^2 + 12*gamma + 6 - Pi^2) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, May 15 2022
%F A317280 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 19 2023
%p A317280 a:=series(1/(1 - log(1 + x))^2, x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # _Paolo P. Lava_, Mar 26 2019
%t A317280 nmax = 24; CoefficientList[Series[1/(1 - Log[1 + x])^2, {x, 0, nmax}], x] Range[0, nmax]!
%t A317280 Table[Sum[StirlingS1[n, k] (k + 1)!, {k, 0, n}], {n, 0, 24}]
%Y A317280 Cf. A005444, A005649, A006252, A052801, A089064.
%Y A317280 Cf. A006252, A354120, A354121.
%K A317280 sign
%O A317280 0,2
%A A317280 _Ilya Gutkovskiy_, Jul 25 2018