A354844 a(n) = n! * Sum_{d|n} (n/d)^d / (d! * (n/d)!).

1, 3, 4, 29, 6, 1027, 8, 26889, 272170, 861851, 12, 515592013, 14, 1530809295, 668366899216, 9382044672017, 18, 1405750464518419, 20, 1393382139935385621, 4274473667143680022, 30537988748467223, 24, 211745638285336995840025

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Formula

E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k!.

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

Mathematica

a[n_] := n! * DivisorSum[n, (n/#)^#/(#! * (n/#)!) &]; Array[a, 25] (* Amiram Eldar, Jun 08 2022 *)

Prog

(PARI) a(n) = n!*sumdiv(n, d, (n/d)^d/(d!*(n/d)!));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k!)))

Crossrefs

Cf. A121860, A354843, A354845.

Sequence in context: A005326 A298561 A226049 * A100600 A345022 A288868

Adjacent sequences: A354841 A354842 A354843 * A354845 A354846 A354847

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2022

Status

approved