A328488 Expansion of e.g.f. 1 / (2 - exp(x * exp(x))).

1, 1, 5, 34, 307, 3456, 46659, 734882, 13227995, 267871036, 6027206803, 149176155030, 4027831914099, 117816299188472, 3711283196035523, 125258162280991858, 4509378597919760779, 172486973301491042964, 6985853719202139488211, 298650859698906574479278

Offset: 0

Author

Ilya Gutkovskiy, Oct 16 2019

Keywords

• nonn

Crossrefs

Cf. A000248, A000670, A003725, A007550, A083355, A292952.

Programs

Mathematica

nmax = 19; CoefficientList[Series[1/(2 - Exp[x Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000248(k) * a(n-k).

a(n) ~ n! / (2*log(2) * (1 + LambertW(log(2))) * LambertW(log(2))^n). - Vaclav Kotesovec, Oct 17 2019