A362085 a(n) = Sum_{k=0..n} (-1)^k * binomial(-3,k) * binomial(n*k,n-k).

1, 3, 12, 55, 315, 2106, 15946, 134730, 1253637, 12702961, 138955146, 1629581955, 20371061009, 270124999977, 3783651174906, 55780472480036, 862795543656489, 13963065117796548, 235845816764772718, 4148499020022749151, 75841424406989195136

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..492

Formula

a(n) = Sum_{k=0..n} binomial(k+2,k) * binomial(n*k,n-k).

a(n) = [x^n] 1/(1 - x*(1+x)^n)^3.

Prog

(PARI) a(n) = sum(k=0, n, binomial(k+2, k)*binomial(n*k, n-k));

Crossrefs

Column k=3 of A362079.

Cf. A000217, A362088.

Sequence in context: A350265 A263533 A064314 * A185630 A284843 A107318

Adjacent sequences: A362082 A362083 A362084 * A362086 A362087 A362088

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2023

Status

approved