A356662 a(n) = n! * Sum_{d|n} 1/(d!)^(n/d - 1).

1, 4, 12, 60, 240, 1740, 10080, 87360, 735840, 7514640, 79833600, 976686480, 12454041600, 175736040480, 2616448554720, 42011071502400, 711374856192000, 12830610027755520, 243290200817664000, 4870565189425615680, 102182981410948838400, 2249099140674523737600

Offset: 1

Author

Seiichi Manyama, Aug 21 2022

Keywords

• nonn

Crossrefs

Cf. A061095, A098558, A356543, A356661.

Programs

Mathematica

a[n_] := n! * DivisorSum[n, 1/(#!)^(n/# - 1) &]; Array[a, 22] (* Amiram Eldar, Aug 21 2022 *)

PARI

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

PARI

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

Formula

a(p) = 2 * p! for prime p.

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