A383536 a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,k)^2 * binomial(n-k,k).

1, 1, 10, 33, 301, 1468, 12006, 70945, 548218, 3588451, 27033942, 187329660, 1398372925, 10015968040, 74666604910, 545706810657, 4076875022533, 30186038308420, 226302738440884, 1690539173230083, 12722171581599588, 95650154853862786, 722460110890588300

Offset: 0

Author

Seiichi Manyama, Apr 29 2025

Keywords

• nonn

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - z^2).

Crossrefs

Cf. A112019.

Programs

PARI

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