A370603 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).

1, 4, 9, 40, 125, 936, 5047, 42848, 367929, 3668500, 39916811, 480577032, 6227020813, 87197480384, 1307761815375, 20923593490816, 355687428096017, 6402405005606628, 121645100408832019, 2432903231908929800, 51090944698284691221, 1124000756238680570272

Offset: 1

Author

Seiichi Manyama, Feb 23 2024

Keywords

• nonn

Crossrefs

Cf. A370579, A370602.

Cf. A370608.

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 * A370608(n).

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

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