A352869 Expansion of e.g.f. 1/(1 - Sum_{k>=1} mu(k) * x^k/k!), where mu() is the Moebius function (A008683).

1, 1, 1, -1, -14, -71, -201, 559, 14152, 125772, 568873, -2930247, -100950588, -1263405885, -7645798213, 62733063199, 2644646815760, 42203809509047, 312892097907012, -3774840465405301, -184229592151309092, -3541775382376189109, -30473600413019593651

Offset: 0

Author

Seiichi Manyama, Apr 06 2022

Keywords

• sign

Crossrefs

Cf. A008683, A300663, A300673.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, moebius(k)*x^k/k!))))

PARI

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

Formula

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