A358410 - OEIS

A358410

a(n) = Sum_{d|n} (d + n/d - 2)!/(d - 1)!.

1, 2, 3, 9, 25, 130, 721, 5069, 40333, 363006, 3628801, 39917607, 479001601, 6227025848, 87178291591, 1307674408449, 20922789888001, 355687428461452, 6402373705728001, 121645100412461861, 2432902008176660217, 51090942171749356812, 1124000727777607680001

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

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

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

MATHEMATICA

a[n_] := DivisorSum[n, (# + n/# - 2)!/(# - 1)! &]; Array[a, 23] (* Amiram Eldar, Aug 30 2023 *)

PROG

(PARI) a(n) = sumdiv(n, d, (d+n/d-2)!/(d-1)!);