A354849 a(n) = (n-1)! * Sum_{d|n} d^(n/d) / (d-1)!.

1, 3, 5, 34, 29, 1626, 727, 99128, 584649, 12353050, 3628811, 4648976652, 479001613, 803709466574, 11133394272015, 391883024332816, 20922789888017, 312756670075449618, 6402373705728019, 148614866400768768020, 2663970255433783296021

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

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

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

Mathematica

a[n_] := (n - 1)! * DivisorSum[n, #^(n/#)/(# - 1)! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)

Prog

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

Crossrefs

Cf. A087906.

Sequence in context: A332704 A263295 A222484 * A222630 A187993 A221158

Adjacent sequences: A354846 A354847 A354848 * A354850 A354851 A354852

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2022

Status

approved