A363666 a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+n-2,n-1).
1, 3, 7, 29, 71, 355, 925, 4425, 13276, 60111, 184757, 856357, 2704157, 12137147, 40367461, 176999505, 601080391, 2616894901, 9075135301, 38884056181, 138014377810, 583674491643, 2104098963721, 8823912454489, 32247616479976, 133998376789707
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n - 2, n - 1] &]; 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-2, n-1));
Formula
a(n) = [x^n] Sum_{k>0} x^k/(1 - k*x^k)^n.