A338684 a(n) = Sum_{d|n} (-1)^(d-1) * (n/d)^n * binomial(d+n/d-1, d).
1, 7, 82, 975, 15626, 275817, 5764802, 133561087, 3486981232, 99853521768, 3138428376722, 106947820494048, 3937376385699290, 155549105311903523, 6568409424129452048, 295137771929866797055, 14063084452067724991010, 708228596784096039676230, 37589973457545958193355602
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)
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PARI
a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-1, d));
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PARI
N=20; x='x+O('x^N); Vec(sum(k=1, N, 1-1/(1+(k*x)^k)^k))
Formula
G.f.: Sum_{k >= 1} (1 - 1/(1 + (k * x)^k)^k).
If p is prime, a(p) = (-1)^(p-1) + p^(p+1).