A352271 Expansion of e.g.f. 1/(2 - exp(x) - log(1 + x)).

1, 2, 8, 51, 427, 4485, 56461, 829619, 13929175, 263120293, 5522411441, 127497249825, 3211140897757, 87615489275587, 2574463431688695, 81050546853002151, 2721785052811891411, 97113737702073060713, 3668859532725782696709, 146306156466305491481253

Offset: 0

Author

Seiichi Manyama, Mar 10 2022

Keywords

• nonn

Crossrefs

Cf. A000670, A007840, A352147, A352270.

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, ((-1)^(k-1)*(k-1)!+1)*binomial(n, k)*a(n-k)));

Formula

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