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%I #17 Apr 24 2021 09:57:13
%S 1,7,82,975,15626,275817,5764802,133561087,3486981232,99853521768,
%T 3138428376722,106947820494048,3937376385699290,155549105311903523,
%U 6568409424129452048,295137771929866797055,14063084452067724991010,708228596784096039676230,37589973457545958193355602
%N a(n) = Sum_{d|n} (-1)^(d-1) * (n/d)^n * binomial(d+n/d-1, d).
%F G.f.: Sum_{k >= 1} (1 - 1/(1 + (k * x)^k)^k).
%F If p is prime, a(p) = (-1)^(p-1) + p^(p+1).
%t a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* _Amiram Eldar_, Apr 24 2021 *)
%o (PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-1, d));
%o (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, 1-1/(1+(k*x)^k)^k))
%Y Cf. A338663, A338682, A338683, A338685, A338689.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 23 2021
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