A352138 Expansion of e.g.f. 1/(exp(x) - log(1 + x)).

1, 0, -2, 1, 17, -17, -401, 817, 16197, -49861, -1123633, 5354787, 105696447, -682603651, -14697824519, 131535803133, 2457119246745, -28321054685609, -572811846560453, 8626026427105983, 146289547341006011, -2784279036040263575, -51756654994427512331

Offset: 0

Author

Seiichi Manyama, Mar 06 2022

Keywords

• sign

Crossrefs

Cf. A352139, A352146, A352147.

Cf. A235378.

Programs

Mathematica

m = 22; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 + x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-log(1+x))))

PARI

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

Formula

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