A377530 - OEIS

%I #12 Oct 31 2024 13:13:31

%S 1,3,18,141,1380,16095,217458,3335745,57225528,1085066523,22526087070,

%T 508042140573,12367076890644,323130848000727,9018976230237834,

%U 267789942962863065,8427492557547704688,280194087519310655667,9813332205452943323190,361109786425470021564021

%N Expansion of e.g.f. 1/(1 - x * exp(x))^3.

%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(k+2,2)/(n-k)!.

%F a(n) ~ n! * n^2 / (2 * (1+LambertW(1))^3 * LambertW(1)^n). - _Vaclav Kotesovec_, Oct 31 2024

%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+2, 2)/(n-k)!);

%Y Cf. A006153, A377529.

%Y Cf. A377532, A377534.

%Y Cf. A377504.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Oct 30 2024