A370605 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)!^d).

1, 3, 4, 11, 6, 72, 8, 499, 850, 4988, 12, 142232, 14, 949392, 7385394, 26739587, 18, 1462302432, 20, 21233776156, 253684768502, 151243121780, 24, 104533367794192, 25973364296906, 102776106948752, 26798029481115778, 95394359150584904, 30

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

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

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. A370581.

Sequence in context: A056045 A360794 A220848 * A232891 A096223 A232862

Adjacent sequences: A370602 A370603 A370604 * A370606 A370607 A370608

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2024

Status

approved