A363668 a(n) = Sum_{d|n} (n/d)^d * binomial(d+n-1,d).
1, 7, 19, 91, 151, 1135, 1765, 12355, 28846, 157917, 352837, 2280955, 5200469, 29986201, 80469589, 427061795, 1166803399, 6211188028, 17672632261, 89483074521, 271071666724, 1316291647997, 4116715364329, 19595444140771, 63205674328876, 292318539358879
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + n - 1, #] &]; Array[a, 30] (* Amiram Eldar, Jul 12 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^d*binomial(d+n-1, d));
Formula
a(n) = [x^n] Sum_{k>0} (1/(1 - k*x^k)^n - 1).