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A354889
a(n) = n! * Sum_{d|n} d^(d-1) / d!.
2
1, 4, 15, 112, 745, 10296, 122689, 2285312, 43953921, 1026157600, 25977341401, 751135431168, 23304312143281, 795924137531264, 29203006015310625, 1154107395053387776, 48661547563094964481, 2186762596692631699968, 104127471943011650364841
OFFSET
1,2
LINKS
FORMULA
E.g.f.: Sum_{k>0} k^(k-1) * x^k/(k! * (1 - x^k)).
If p is prime, a(p) = p^(p-1) + p!.
MATHEMATICA
a[n_] := n! * DivisorSum[n, #^(# - 1)/#! &]; Array[a, 19] (* Amiram Eldar, Jun 10 2022 *)
PROG
(PARI) a(n) = n!*sumdiv(n, d, d^(d-1)/d!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^(k-1)*x^k/(k!*(1-x^k)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 10 2022
STATUS
approved