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 A382840 #6 Apr 10 2025 03:25:44
%S A382840 1,1,4,30,316,4290,71268,1400112,31750416,816215760,23455342560,
%T A382840 745073660496,25924233481056,980518650296640,40054724743501440,
%U A382840 1757539560656401920,82439565962427760896,4116529729771939393920,218017561353648160158720,12206586491422209675532800
%N A382840 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * Stirling1(n,k) * k!.
%F A382840 a(n) = n! * [x^n] 1 / (1 - log(1 + x))^n.
%F A382840 a(n) ~ n^n / (sqrt(1 + LambertW(1)) * 2^n * exp(n) * (cosh(LambertW(1)) - 1)^n). - _Vaclav Kotesovec_, Apr 07 2025
%t A382840 Table[Sum[Binomial[n + k - 1, k] StirlingS1[n, k] k!, {k, 0, n}], {n, 0, 19}]
%t A382840 Table[n! SeriesCoefficient[1/(1 - Log[1 + x])^n, {x, 0, n}], {n, 0, 19}]
%Y A382840 Cf. A006252, A305919, A308565, A317280, A354120, A354121, A382830.
%K A382840 nonn
%O A382840 0,3
%A A382840 _Ilya Gutkovskiy_, Apr 06 2025