A352295 Expansion of e.g.f. 1/(exp(x) - x/(1 + x)).

1, 0, -3, 5, 29, -181, -401, 9645, -14183, -689257, 4826171, 55700633, -1024570955, -2770525005, 221566919911, -1028838834811, -49439771820367, 723165789334703, 9903852025111027, -362150510124039471, -463774017017434739, 169793689786411161995

Offset: 0

Author

Seiichi Manyama, Mar 11 2022

Keywords

• sign

Crossrefs

Cf. A352138, A352293, A352294.

Programs

Mathematica

m = 21; Range[0, m]! * CoefficientList[Series[1/(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/(exp(x)-x/(1+x))))

PARI

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

Formula

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