A383524 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n-k,k)^2.

1, 1, 3, 13, 43, 171, 711, 2913, 12363, 53203, 230593, 1010703, 4463119, 19827679, 88594299, 397741893, 1793063883, 8113429419, 36832823289, 167701920759, 765577205433, 3503296744233, 16065995216109, 73824301464939, 339844364816559, 1567063753104471, 7237078197034221

Offset: 0

Author

Seiichi Manyama, Apr 29 2025

Keywords

• nonn
• changed

Comments

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

Crossrefs

Cf. A000172, A181545, A275027.

Programs

Mathematica

Table[Sum[Binomial[n,k] * Binomial[n-k,k]^2,{k,0,n}], {n,0,30}] (* Vaclav Kotesovec, Aug 30 2025 *)

PARI

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