A354509 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(d+1)/(d * (k/d)!) )/(n-k)!.

1, 2, 6, 5, 5, -8, 560, -5997, -14765, 176826, 5206410, -42491623, -427057527, -412183484, 147180377804, -569782989113, -8367671807033, -119681999820906, 4440973420854454, -121033449284728099, 49772248126885197, 36615485147317407728, 1696495197400394891912

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = Sum_{k=1..n} A352013(k) * binomial(n,k).

E.g.f.: -exp(x) * Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k.

E.g.f.: exp(x) * Sum_{k>0} log(1+x^k)/k!.

Prog

(PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!))/(n-k)!);
(PARI) a352013(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
a(n) = sum(k=1, n, a352013(k)*binomial(n, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, log(1+x^k)/k!)))

Crossrefs

Cf. A352013, A354505, A356401.

Sequence in context: A273621 A190124 A067548 * A245698 A053793 A371324

Adjacent sequences: A354506 A354507 A354508 * A354510 A354511 A354512

Keyword

sign

Author

Seiichi Manyama, Aug 15 2022

Status

approved