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

0,3

Comments

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

Links

Table of n, a(n) for n=0..26.

Mathematica

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

Prog

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

Crossrefs

Cf. A000172, A181545, A275027, A356521.

Sequence in context: A054771 A258776 A201710 * A019008 A062609 A004660

Adjacent sequences: A383521 A383522 A383523 * A383525 A383526 A383527

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2025

Status

approved