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 A358741 #12 Feb 18 2023 03:26:54
%S A358741 1,1,9,179,6655,400581,35530421,4357960999,706230728379,
%T A358741 146116931998025,37577989723572001,11758017370126904091,
%U A358741 4398121660346674034039,1938019214715102033590029,993580299268226843514372045,586357970017371399763899232271
%N A358741 Expansion of Sum_{k>=0} k! * ( k * x/(1 - x) )^k.
%F A358741 a(n) = Sum_{k=1..n} k! * k^k * binomial(n-1,k-1) for n > 0.
%F A358741 a(n) ~ n! * n^n. - _Vaclav Kotesovec_, Feb 18 2023
%t A358741 nmax = 20; CoefficientList[1 + Series[Sum[k! * (k * x/(1 - x))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 18 2023 *)
%o A358741 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*(k*x/(1-x))^k))
%o A358741 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k!*k^k*binomial(n-1, k-1)));
%Y A358741 Cf. A358738, A358740.
%Y A358741 Cf. A355494.
%K A358741 nonn
%O A358741 0,3
%A A358741 _Seiichi Manyama_, Nov 29 2022