A363697 a(n) = -n! * Sum_{d|n} (-n/d)^d / d!.
1, 3, 19, 47, 601, 2039, 35281, -26881, 4898881, -8104321, 439084801, 576132479, 80951270401, -913158005761, 49506372115201, -558073906790401, 6046686277632001, 79958674981785599, 2311256907767808001, -115583806104986419201
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..447
Programs
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Mathematica
a[n_] := -n! * DivisorSum[n, (-n/#)^#/#! &]; Array[a, 20] (* Amiram Eldar, Jul 03 2023 *)
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PARI
a(n) = -n!*sumdiv(n, d, (-n/d)^d/d!);
Formula
E.g.f.: Sum_{k>0} (1 - exp(-k * x^k)).
If p is prime, a(p) = (-1)^(p+1) + p * p!.