A336712 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} 2^(n-k) * binomial(n,k) * binomial(n+(n-1)*k,k-1) for n > 0.

1, 1, 4, 30, 364, 6502, 158034, 4921112, 187897728, 8519286854, 447829041358, 26796275824186, 1798936842255128, 133933302810144684, 10953460639289615412, 976226180855018504472, 94181146038753255120480, 9778885058353578446996934, 1087326670244362420301889926

Offset

0,3

Links

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

Mathematica

a[0] = 1; a[n_] := Sum[2^(n - k) * Binomial[n, k] * Binomial[n + (n - 1)*k, k - 1], {k, 1, n}] / n; Array[a, 19, 0] (* Amiram Eldar, Aug 01 2020 *)

Prog

(PARI) {a(n) = if(n==0, 1, sum(k=1, n, 2^(n-k)*binomial(n, k)*binomial(n+(n-1)*k, k-1))/n)}

Crossrefs

Main diagonal of A336707.

Cf. A336578, A335871, A336713, A336714.

Sequence in context: A295899 A291060 A166892 * A185523 A187736 A199569

Adjacent sequences: A336709 A336710 A336711 * A336713 A336714 A336715

Keyword

nonn

Author

Seiichi Manyama, Aug 01 2020

Status

approved