A368176 - OEIS

%I #14 Mar 11 2024 05:05:19

%S 0,1,5,26,182,1704,19992,281392,4620464,86707584,1830550400,

%T 42940149504,1107995749632,31188982438912,951100528802816,

%U 31234626965637120,1099029746752575488,41248797730190032896,1644909773059509682176

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

%F a(n) = Sum_{k=1..n} (2*k)^(n-k) * (k-1)! * binomial(n,k).

%F a(n) ~ (n-1)! * 2^n / LambertW(2)^n. - _Vaclav Kotesovec_, Mar 11 2024

%o (PARI) a(n) = sum(k=1, n, (2*k)^(n-k)*(k-1)!*binomial(n, k));

%Y Cf. A009306, A009444, A368177.

%Y Cf. A336950.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Dec 14 2023