A383537 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k,k)^2 * binomial(n-2*k,k).

1, 1, 1, 17, 51, 109, 981, 4209, 12637, 79351, 393493, 1454021, 7686459, 39697057, 166999101, 823144689, 4241896917, 19293138685, 93151760599, 473739765167, 2252548154403, 10877558634801, 54682637188009, 266304982300197, 1295171619802551, 6466091747859771

Offset: 0

Author

Seiichi Manyama, Apr 29 2025

Keywords

• nonn

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - z^3).

Crossrefs

Cf. A383538.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(n+k, k)^2*binomial(n-2*k, k));