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
Keywords
Programs
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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]] -
PARI
a(n) = sumdiv(n, d, (-1)^(n/d+1)*d!); \\ Michel Marcus, Nov 12 2018
Formula
G.f.: Sum_{k>=1} k!*x^k/(1 + x^k).
a(n) ~ n!. - Vaclav Kotesovec, Nov 13 2018