A370604 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)^d).

1, 3, 5, 16, 29, 251, 727, 7988, 47049, 512767, 3628811, 58012582, 479001613, 8007115559, 92633212687, 1648230784216, 20922789888017, 449622885136443, 6402373705728019, 146721895942876274, 2507411046373376021, 60380204535989936347, 1124000727777607680023

Offset: 1

Author

Seiichi Manyama, Feb 23 2024

Keywords

• nonn

Crossrefs

Cf. A370580.

Programs

PARI

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

PARI

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

Formula

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

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