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 A305981 #18 Feb 16 2025 08:33:54
%S A305981 1,1,5,41,468,6854,122582,2589978,63129392,1743732192,53827681152,
%T A305981 1836453542472,68620052332752,2786929842106344,122241516227220504,
%U A305981 5758920745460806824,290017142065771138560,15547326972257789803200,883974436758296523437760,53131928820278417749940544,3366145488853852112016117504
%N A305981 Expansion of e.g.f. 1/(1 + LambertW(log(1 - x))).
%H A305981 Seiichi Manyama, <a href="/A305981/b305981.txt">Table of n, a(n) for n = 0..376</a>
%H A305981 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A305981 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*k^k.
%F A305981 a(n) ~ n^n / ((exp(exp(-1)) - 1)^(n + 1/2) * exp(n*(1 - exp(-1)) + 1/2)). - _Vaclav Kotesovec_, Aug 18 2018
%p A305981 a:=series(1/(1+LambertW(log(1-x))),x=0,21): seq(n!*coeff(a,x,n),n=0..20); # _Paolo P. Lava_, Mar 26 2019
%t A305981 nmax = 20; CoefficientList[Series[1/(1 + LambertW[Log[1 - x]]), {x, 0, nmax}], x] Range[0, nmax]!
%t A305981 Join[{1}, Table[Sum[Abs[StirlingS1[n, k]] k^k, {k, n}], {n, 20}]]
%o A305981 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^k*stirling(n, k, 1)); \\ _Seiichi Manyama_, Feb 05 2022
%o A305981 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(log(1-x))))) \\ _Seiichi Manyama_, Feb 05 2022
%Y A305981 Cf. A000312, A052807, A277489, A282190, A305819.
%K A305981 nonn
%O A305981 0,3
%A A305981 _Ilya Gutkovskiy_, Aug 18 2018