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

0,5

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

(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)));

Crossrefs

Cf. A008683, A300663, A300673.

Sequence in context: A245950 A041372 A245951 * A212572 A186707 A212752

Adjacent sequences: A352866 A352867 A352868 * A352870 A352871 A352872

Keyword

sign

Author

Seiichi Manyama, Apr 06 2022

Status

approved