A343549 a(n) = n * Sum_{d|n} binomial(d+n-1,n)/d.

1, 5, 13, 49, 131, 545, 1723, 6809, 24484, 94445, 352727, 1366273, 5200313, 20135939, 77571083, 301034537, 1166803127, 4540794476, 17672631919, 68943346009, 269129827042, 1052178506615, 4116715363823, 16124644677569, 63205303337656, 247964681424725, 973469783435197

Offset

1,2

Links

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

Formula

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

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

From Seiichi Manyama, Jun 14 2023: (Start)

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A038040, A309731, A343544, A343545, A343546, A343547, A343548.

Sequence in context: A082132 A220900 A138277 * A084601 A149532 A149533

Adjacent sequences: A343546 A343547 A343548 * A343550 A343551 A343552

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2021

Status

approved