A335871 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.

1, 1, 3, 20, 234, 4159, 101538, 3182454, 122285201, 5575750271, 294529785168, 17697480642005, 1192398100081202, 89053864927236146, 7302988011333915878, 652439391227186881683, 63077327237347821501754, 6561701255914880362990927, 730833849063629052249986940

Offset: 0

Author

Seiichi Manyama, Aug 01 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..339

Crossrefs

Main diagonal of A336706.

Cf. A336578, A336712, A336713, A336714.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[Binomial[n, k] * Binomial[n + (n - 1)*k, k - 1], {k, 1, n}] / n; Array[a, 19, 0] (* Amiram Eldar, Aug 01 2020 *)

PARI

{a(n) = if(n==0, 1, sum(k=1, n, binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)}