A352292 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 - x)).

1, 2, 11, 91, 1007, 13941, 231645, 4490739, 99496787, 2480012329, 68684121713, 2092433179431, 69540117508119, 2503694594140845, 97076021030158565, 4032791843669289883, 178701570260701316219, 8413561430997560725713, 419425619946011214516345

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• nonn

Crossrefs

Cf. A002866, A352270, A352293.

Programs

Mathematica

m = 18; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 - x)), {x, 0, m}], x] (* Amiram Eldar, Mar 11 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1-x))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, (k!+1)*binomial(n, k)*a(n-k)));

Formula

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