A354507 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d )/(k * (n-k)!).

1, 3, 14, 48, 269, 1615, 12662, 73528, 836817, 8476243, 99348534, 948849176, 13193115597, 177346261391, 3684976294222, 45021819481808, 734808219625345, 13524660020400771, 290452222949307070, 4639956700466396256, 128621330002689008237, 2735863084773695212719

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

a(n) = n! * Sum_{k=1..n} A000593(k)/(k * (n-k)!).

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

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

Prog

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

Crossrefs

Cf. A354506, A354508.

Cf. A000593, A356390.

Sequence in context: A176027 A345690 A139263 * A337075 A261043 A063025

Adjacent sequences: A354504 A354505 A354506 * A354508 A354509 A354510

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved