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

1,2

Links

Table of n, a(n) for n=1..23.

Formula

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

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

Prog

(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))))

Crossrefs

Cf. A370580.

Sequence in context: A080056 A330055 A019096 * A295358 A369930 A077551

Adjacent sequences: A370601 A370602 A370603 * A370605 A370606 A370607

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2024

Status

approved