A352139 Expansion of e.g.f. 1/(exp(x) - log(1 - x)).

1, -2, 6, -27, 161, -1205, 10799, -113043, 1351461, -18183781, 271784079, -4469044657, 80160267791, -1557710354083, 32597642189657, -730897865864471, 17480390183397209, -444198879957594857, 11951585821669838395, -339434402344422296117

Offset: 0

Author

Seiichi Manyama, Mar 06 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..421

Crossrefs

Cf. A352138, A352146, A352147.

Cf. A006252, A038507.

Programs

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - Log[1 - x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)

PARI

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

PARI

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

Formula

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