A354898 a(n) = n! * Sum_{d|n} d^(n - d) / (d! * (n/d)!).

1, 2, 2, 26, 2, 2582, 2, 268802, 7348322, 51120722, 2, 299332756802, 2, 7157951760962, 18701679546950402, 613777679843328002, 2, 3250742570192384467202, 2, 29411516073133093829529602, 1146522800008167069616128002, 4017001663590220290585602, 2

Offset: 1

Author

Seiichi Manyama, Jun 11 2022

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..305

Crossrefs

Cf. A121860, A354845, A354891, A354893, A354897.

Programs

Maple

f:= proc(n) local d; n! * add(d^(n-d)/(d! * (n/d)!), d = numtheory:-divisors(n)) end proc:
map(f, [$1..30]); # Robert Israel, Jul 10 2023

Mathematica

a[n_] := n! * DivisorSum[n, #^(n - #)/(#! * (n/#)!) &]; Array[a, 23] (* Amiram Eldar, Jun 11 2022 *)

PARI

a(n) = n!*sumdiv(n, d, d^(n-d)/(d!*(n/d)!));

PARI

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

Formula

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

If p is prime, a(p) = 2.