A321521 a(n) = Sum_{d|n} (-1)^(n/d+1)*d!.

1, 1, 7, 21, 121, 715, 5041, 40293, 362887, 3628681, 39916801, 479000895, 6227020801, 87178286161, 1307674368127, 20922789847653, 355687428096001, 6402373705365835, 121645100408832001, 2432902008173011101, 51090942171709445047, 1124000727777567763201

Offset

1,3

Links

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

Formula

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

a(n) ~ n!. - Vaclav Kotesovec, Nov 13 2018

Mathematica

Table[Sum[(-1)^(n/d + 1) d!, {d, Divisors[n]}], {n, 22}]
nmax = 22; Rest[CoefficientList[Series[Sum[k! x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d!); \\ Michel Marcus, Nov 12 2018

Crossrefs

Cf. A000142, A062363, A321522.

Sequence in context: A038184 A001185 A001693 * A061961 A028248 A267609

Adjacent sequences: A321518 A321519 A321520 * A321522 A321523 A321524

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 12 2018

Status

approved