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 A377530 #15 Feb 05 2025 22:04:14
%S A377530 1,3,18,141,1380,16095,217458,3335745,57225528,1085066523,22526087070,
%T A377530 508042140573,12367076890644,323130848000727,9018976230237834,
%U A377530 267789942962863065,8427492557547704688,280194087519310655667,9813332205452943323190,361109786425470021564021
%N A377530 Expansion of e.g.f. 1/(1 - x * exp(x))^3.
%F A377530 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+2,2)/(n-k)!.
%F A377530 a(n) ~ n! * n^2 / (2 * (1+LambertW(1))^3 * LambertW(1)^n). - _Vaclav Kotesovec_, Oct 31 2024
%t A377530 nmax=19; CoefficientList[Series[1/(1 - x * Exp[x])^3,{x,0,nmax}],x]Range[0,nmax]! (* _Stefano Spezia_, Feb 05 2025 *)
%o A377530 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+2, 2)/(n-k)!);
%Y A377530 Cf. A006153, A377529.
%Y A377530 Cf. A377532, A377534.
%Y A377530 Cf. A377504.
%K A377530 nonn,easy
%O A377530 0,2
%A A377530 _Seiichi Manyama_, Oct 30 2024