A343548 a(n) = Sum_{d|n} binomial(d+n-1,n).

1, 4, 11, 41, 127, 498, 1717, 6610, 24366, 93391, 352717, 1358826, 5200301, 20097076, 77562773, 300786339, 1166803111, 4539163784, 17672631901, 68933291834, 269129233484, 1052113994124, 4116715363801, 16124221819056, 63205303242628, 247961973949228, 973469736360283

Offset

1,2

Links

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

Formula

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

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

Mathematica

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

Prog

(PARI) a(n) = sumdiv(n, d, binomial(d+n-1, n));

Crossrefs

Cf. A000005, A000203, A007437, A059358, A073570, A101289, A332508, A343549.

Sequence in context: A228190 A289283 A152532 * A121096 A047091 A121092

Adjacent sequences: A343545 A343546 A343547 * A343549 A343550 A343551

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2021

Status

approved