A383525 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k)^2 * binomial(n-2*k,k).

1, 1, 1, 10, 33, 76, 370, 1569, 5089, 20584, 88776, 336865, 1336434, 5639869, 22824789, 92230285, 384930529, 1595575648, 6570596764, 27418859721, 114736740808, 478594009281, 2005907811469, 8437974722463, 35480386059826, 149466347150701, 631299305598625, 2668522402478179

Offset: 0

Author

Seiichi Manyama, Apr 29 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000172, A248658, A383526.

Programs

PARI

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