A356390 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d + 1) * d ) /k.

1, 3, 17, 74, 514, 3564, 30708, 250704, 2780496, 29982240, 373350240, 4639870080, 67024333440, 988156834560, 16914631507200, 271941778483200, 4999620452198400, 94617104704819200, 1925772463506124800, 39245319872575488000, 902004581585737728000

Offset: 1

Author

Seiichi Manyama, Aug 05 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..448

Crossrefs

Cf. A356389, A356391.

Cf. A000593, A356010, A356393.

Programs

Mathematica

Table[n! * Sum[Sum[(-1)^(k/d + 1)*d, {d, Divisors[k]}]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)

PARI

a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d)/k);

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (-x)^k/(k*(1-x^k)))/(1-x)))

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k))/(1-x)))

Formula

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

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

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

a(n) ~ n! * n * Pi^2/12. - Vaclav Kotesovec, Aug 07 2022