A363737 a(n) = n! * Sum_{d|n} (-1)^(d+1) / (d! * (n/d)!).
1, 0, 2, -6, 2, 0, 2, -1680, 10082, 0, 2, -665280, 2, 0, 3632428802, -36843206400, 2, 0, 2, -670442572800, 3379030566912002, 0, 2, -71812452903064473600, 1077167364120207360002, 0, 10002268381116211200002, -3497296636753920000, 2, 0, 2
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, (-1)^(#+1)/(#! * (n/#)!) &]; Array[a, 30] (* Amiram Eldar, Jul 03 2023 *)
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PARI
a(n) = n!*sumdiv(n, d, (-1)^(d+1)/(d!*(n/d)!));
Formula
E.g.f.: Sum_{k>0} (1 - exp(-x^k))/k!.
If p is an odd prime, a(p) = 2.