A370674 Expansion of Sum_{k>0} k! * x^k/(1+x^k)^(k+1).

1, 0, 9, 14, 125, 702, 5047, 40172, 362949, 3628100, 39916811, 478996746, 6227020813, 87178250922, 1307674370745, 20922789524192, 355687428096017, 6402373702119096, 121645100408832019, 2432902008136718030, 51090942171709621965, 1124000727777128678510

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

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

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

Prog

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

Crossrefs

Cf. A177249, A177251, A177253.

Cf. A344777, A358411.

Sequence in context: A298754 A166654 A348318 * A373330 A131224 A073920

Adjacent sequences: A370671 A370672 A370673 * A370675 A370676 A370677

Keyword

nonn

Author

Seiichi Manyama, Feb 25 2024

Status

approved