A370668 Expansion of Sum_{k>0} k! * ( x * (1+x^k) )^k.

1, 3, 6, 28, 120, 740, 5040, 40416, 362898, 3629400, 39916800, 479006070, 6227020800, 87178326480, 1307674369200, 20922790210656, 355687428096000, 6402373709004720, 121645100408832000, 2432902008212929224, 51090942171709545840, 1124000727778046764800

Offset: 1

Author

Seiichi Manyama, Feb 25 2024

Keywords

• nonn

Crossrefs

Cf. A240172, A370509, A370510.

Cf. A217668.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*(x*(1+x^k))^k))

PARI

a(n) = sumdiv(n,d, d!*binomial(d, n/d-1));

Formula

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

If p is an odd prime, a(p) = p!.