A356015 a(n) = n! * Sum_{k=1..n} 1/(k * floor(n/k)!).

1, 2, 6, 21, 125, 625, 5089, 38185, 343657, 3376081, 40765681, 427649761, 6038448481, 84486386881, 1252766088001, 19388604009601, 350529058051201, 5938944734419201, 119242323659692801, 2303746722596390401, 48358406991122726401, 1063884813011759692801

Offset: 1

Author

Seiichi Manyama, Jul 23 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Plot of a(n)/n! for n = 1..10000

Crossrefs

Cf. A355987, A356011.

Programs

Mathematica

Table[n! * Sum[1 / (k*Floor[n/k]!), {k,1,n}], {n,1,25}] (* Vaclav Kotesovec, Aug 11 2025 *)

PARI

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

PARI

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

Formula

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

Conjecture: a(n) ~ c * n!, where c = 0.95488757... - Vaclav Kotesovec, Aug 11 2025