A370608 a(n) = (n-1)! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).

1, 2, 3, 10, 25, 156, 721, 5356, 40881, 366850, 3628801, 40048086, 479001601, 6228391456, 87184121025, 1307724593176, 20922789888001, 355689166978146, 6402373705728001, 121645161595446490, 2432902128489747201, 51090943465394571376, 1124000727777607680001

Offset: 1

Author

Seiichi Manyama, Feb 23 2024

Keywords

• nonn

Crossrefs

Cf. A005225, A087906.

Cf. A370603.

Programs

PARI

a(n) = (n-1)!*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, (k-1)!*(exp(x^k/k!)-1))))

Formula

If p is prime, a(p) = 1 + (p-1)!.

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