A329966 a(n) = n! * Sum_{d|n} binomial(n-1,d-1) / d!.

1, 3, 7, 61, 121, 3721, 5041, 240241, 2056321, 23768641, 39916801, 11104853761, 6227020801, 683519316481, 32048919302401, 577844178912001, 355687428096001, 261396772808371201, 121645100408832001, 202418558674082150401, 2061884451929702400001, 12935940353987812761601

Offset: 1

Author

Ilya Gutkovskiy, Nov 26 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..447

Crossrefs

Cf. A000262, A056045, A057625, A271654.

Programs

Magma

[Factorial(n)*( &+[ Binomial(n-1,d-1)/Factorial(d):d in Divisors(n)]): n in [1..22]]; // Marius A. Burtea, Jan 02 2020

Maple

N:= 30:
V:= Vector(N):
for d from 1 to N do
   for k from 1 to floor(N/d) do
     n:= k*d; V[n]:= V[n] + n!/d!*binomial(n-1,d-1);
od od:
convert(V,list); # Robert Israel, Jan 01 2020

Mathematica

a[n_] := n! Sum[Binomial[n - 1, d - 1]/d!, {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]

PARI

a(n) = n! * sumdiv(n, d, binomial(n-1,d-1) / d!); \\ Michel Marcus, Nov 26 2019