login
A354851
a(n) = (n-1)! * Sum_{d|n} d^(n/d).
1
1, 3, 8, 54, 144, 2880, 5760, 206640, 1491840, 24675840, 43545600, 10298534400, 6706022400, 1195587993600, 33476463820800, 775450900224000, 376610217984000, 553805325545472000, 128047474114560000, 339876410542276608000, 6208765924866785280000
OFFSET
1,2
FORMULA
a(n) = (n-1)! * A055225(n).
E.g.f.: -Sum_{k>0} log(1 - k * x^k)/k.
If p is prime, a(p) = (p-1)! + p!.
MATHEMATICA
a[n_] := (n - 1)! * DivisorSum[n, #^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
PROG
(PARI) a(n) = (n-1)!*sumdiv(n, d, d^(n/d));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 08 2022
STATUS
approved