A354900 a(n) = n! * Sum_{d|n} d^d / (n/d)!.
1, 9, 163, 6193, 375001, 33602521, 4150656721, 676462516801, 140587148681281, 36288005670120961, 11388728893445164801, 4270826391670469473921, 1886009588552176549862401, 968725766890781857146309121, 572622616354852243874626732801
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 11 2022 *)
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PARI
a(n) = n!*sumdiv(n, d, d^d/(n/d)!);
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1))))
Formula
E.g.f.: Sum_{k>0} k^k * (exp(x^k) - 1).
If p is prime, a(p) = 1 + p^p * p!.