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 A382830 #6 Apr 06 2025 14:57:13
%S A382830 1,1,8,102,1804,40890,1131108,36948240,1391945616,59411849040,
%T A382830 2833582748160,149347596487056,8620256620495584,540775669746661440,
%U A382830 36636074309252234880,2665704585421541790720,207329122282259073044736,17165075378189396045777280,1507206260097615729874083840
%N A382830 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * |Stirling1(n,k)| * k!.
%F A382830 a(n) = n! * [x^n] 1 / (1 + log(1 - x))^n.
%F A382830 a(n) ~ LambertW(exp(2))^n * n^n / (sqrt(1 + LambertW(exp(2))) * exp(n) * (LambertW(exp(2)) - 1)^(2*n)). - _Vaclav Kotesovec_, Apr 06 2025
%t A382830 Table[Sum[Binomial[n + k - 1, k] Abs[StirlingS1[n, k]] k!, {k, 0, n}], {n, 0, 18}]
%t A382830 Table[n! SeriesCoefficient[1/(1 + Log[1 - x])^n, {x, 0, n}], {n, 0, 18}]
%Y A382830 Cf. A007840, A052801, A277759, A305919, A354122, A354123.
%K A382830 nonn
%O A382830 0,3
%A A382830 _Ilya Gutkovskiy_, Apr 06 2025