A368265 - OEIS

%I #12 Dec 29 2023 06:27:08

%S 1,3,12,65,460,4057,42922,529769,7472808,118586033,2090936014,

%T 40554647377,858082563532,19668880007129,485528656965762,

%U 12841428220413593,362276791422785488,10859170086870710497,344648459867067117334,11546148650974694099201

%N Expansion of e.g.f. exp(2*x) / (1 - x*exp(x)).

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

%F a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n+2)). - _Vaclav Kotesovec_, Dec 29 2023

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

%Y Cf. A006153, A072597, A092148, A368266.

%Y Cf. A368267, A368271.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 19 2023