A370602 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)^(d-1)).

1, 4, 9, 40, 125, 1056, 5047, 51248, 383049, 4364020, 39916811, 576885552, 6227020813, 99634224704, 1334500527375, 23592657488416, 355687428096017, 7202890599354468, 121645100408832019, 2679832071577681040, 51612375654647808021, 1226182612423511392672

Offset: 1

Author

Seiichi Manyama, Feb 23 2024

Keywords

• nonn

Crossrefs

Cf. A370579, A370603.

Cf. A005225.

Programs

PARI

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

PARI

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

Formula

a(n) = n * A005225(n).

If p is prime, a(p) = p + p!.

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