A327587 a(n) = n! * Sum_{d|n} (-1)^(n - d) / (n/d)!^d.

1, 1, 7, 29, 121, 649, 5041, 42909, 364561, 3515651, 39916801, 486821873, 6227020801, 86497214231, 1307843292757, 21004582611869, 355687428096001, 6390006277567483, 121645100408832001, 2435277595236694779, 51091124681475552961, 1123451899297248225431

Offset: 1

Author

Ilya Gutkovskiy, Sep 17 2019

Keywords

• nonn

Crossrefs

Cf. A061095, A327243.

Programs

Mathematica

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

PARI

a(n) = n!*sumdiv(n, d, (-1)^(n-d)/(n/d)!^d); \\ Michel Marcus, Sep 19 2019

Formula

E.g.f.: Sum_{k>=1} -(-x)^k / (k! + (-x)^k).

a(p) = p! + 1, where p is odd prime.