A355987 a(n) = n! * Sum_{k=1..n} 1/floor(n/k)!.

1, 3, 13, 61, 421, 2641, 23521, 203281, 2071441, 22407841, 286403041, 3453468481, 51122111041, 759194916481, 12216117513601, 203300293996801, 3811792426041601, 69634723878720001, 1444704854104512001, 29725332567567436801, 658231789483184716801

Offset: 1

Author

Seiichi Manyama, Jul 22 2022

Keywords

• nonn

Crossrefs

Cf. A007489, A081125, A345683, A355886, A355988, A355991.

Programs

Mathematica

a[n_] := n! * Sum[1/Floor[n/k]!, {k, 1, n}]; Array[a, 21] (* Amiram Eldar, Jul 22 2022 *)

PARI

a(n) = n!*sum(k=1, n, 1/(n\k)!);

PARI

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

Formula

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

a(n) ~ c * n! * n, where c = 0.59962032... - Vaclav Kotesovec, Aug 03 2022

Conjecture: c = Sum_{k>=1} 1/((k+1)!*k) = 2 - exp(1) - A001620 + A091725. - Vaclav Kotesovec, Sep 24 2023