A355991 a(n) = n! * Sum_{k=1..n} 1/(k! * floor(n/k)!).

1, 2, 5, 12, 57, 158, 1101, 5442, 28811, 212502, 2337513, 9422306, 122489967, 1654319046, 13917499277, 111631450818, 1897734663891, 23705612782022, 450406642858401, 3091477152208002, 51404897928720023, 1130752882197523686, 26007316290543044757

Offset: 1

Author

Seiichi Manyama, Jul 22 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..464

Crossrefs

Row sums of A355996.

Cf. A121860, A355886, A355987, A355989, A355990.

Programs

Mathematica

a[n_] := n! * Sum[1/(k! * Floor[n/k]!), {k, 1, n}]; Array[a, 23] (* Amiram Eldar, Jul 22 2022 *)

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!.