A343547 a(n) = n * Sum_{d|n} binomial(d+n-2,n-1)/d.

1, 4, 9, 32, 75, 318, 931, 3712, 13014, 50110, 184767, 715656, 2704169, 10454976, 40126395, 155462016, 601080407, 2335849578, 9075135319, 35359120940, 137847221148, 538346579034, 2104098963743, 8234009441952, 32247603785500, 126414311404108, 495918587420145

Offset: 1

Author

Seiichi Manyama, Apr 19 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A038040, A309731, A332508, A343544, A343545, A343546.

Programs

Mathematica

a[n_] := n * DivisorSum[n, Binomial[# + n - 2, n-1]/# &]; Array[a, 30] (* Amiram Eldar, Apr 25 2021 *)

PARI

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

Formula

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

a(n) = [x^n] Sum_{k>=1} binomial(k+n-2,n-1) * x^k/(1 - x^k)^2.