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 A358740 #11 Feb 18 2023 03:22:52
%S A358740 1,1,9,195,7699,482309,43994741,5508667927,906931827831,
%T A358740 189998213001033,49359340639141993,15573690455085072011,
%U A358740 5866304418414451865723,2600416934781350100016717,1340037064604153376788884701,794358527033920600533985973631
%N A358740 Expansion of Sum_{k>=0} k! * ( k * x/(1 - k*x) )^k.
%F A358740 a(n) = Sum_{k=1..n} k! * k^n * binomial(n-1,k-1) for n > 0.
%F A358740 a(n) ~ exp(exp(-1)) * n! * n^n. - _Vaclav Kotesovec_, Feb 18 2023
%t A358740 nmax = 20; CoefficientList[1 + Series[Sum[k! * (k * x/(1 - k*x))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 18 2023 *)
%o A358740 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*(k*x/(1-k*x))^k))
%o A358740 (PARI) a(n) = if(n==0, 1, sum(k=1, n, k!*k^n*binomial(n-1, k-1)));
%Y A358740 Cf. A358738, A358741.
%Y A358740 Cf. A195242.
%K A358740 nonn
%O A358740 0,3
%A A358740 _Seiichi Manyama_, Nov 29 2022