A352270 Expansion of e.g.f. 1/(2 - exp(x) + log(1 - x)).

1, 2, 10, 75, 751, 9405, 141361, 2478959, 49683047, 1120216645, 28064294201, 773391141325, 23250533411821, 757231705088131, 26558855360366239, 998051946325525971, 40006049065833007891, 1703833370634756077097, 76833773059665726636621

Offset: 0

Author

Seiichi Manyama, Mar 10 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..390

Crossrefs

Cf. A000670, A352139, A352146, A352271.

Programs

PARI

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