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

1,2

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = [x^n] Sum_{k>0} x^k/(1 - k*x^k)^n.

Mathematica

a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n - 2, n - 1] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n-2, n-1));

Crossrefs

Cf. A167531, A363642, A363645.

Cf. A332508, A363663, A363667.

Sequence in context: A171134 A080806 A321191 * A148759 A148760 A148761

Adjacent sequences: A363663 A363664 A363665 * A363667 A363668 A363669

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2023

Status

approved