A370579 a(n) = n! * Sum_{d|n} 1/(d-1)!.

1, 4, 9, 52, 125, 1806, 5047, 87368, 544329, 7408810, 39916811, 1281329292, 6227020813, 174477663374, 2015997984015, 45336862771216, 355687428096017, 16059446167564818, 121645100408832019, 5372665305815808020, 76707372899469312021, 2248001765299683993622

Offset: 1

Author

Seiichi Manyama, Feb 23 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A087906, A370580.

Cf. A370602, A370603.

Programs

PARI

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

PARI

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

Formula

a(n) = n * A087906(n).

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

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