A363663 a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-1,n).
1, 4, 11, 46, 127, 596, 1717, 7792, 24806, 108450, 352717, 1563914, 5200301, 22539046, 77876117, 331982444, 1166803111, 4945693769, 17672631901, 74053888812, 269344740908, 1118110015874, 4116715363801, 16984153623296, 63205318063252, 259049084680612
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n - 1, n] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)
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PARI
a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n-1, n));
Formula
a(n) = [x^n] Sum_{k>0} x^k/(1 - k*x^k)^(n+1).