A378406 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n+2*k,n-2*k).

1, 1, 3, 16, 67, 266, 1116, 4803, 20707, 89665, 390868, 1712283, 7527664, 33196606, 146800811, 650724896, 2890442051, 12862496583, 57331583055, 255915024714, 1143845768892, 5118643987872, 22930389117771, 102824420890590, 461502269341936, 2073064313021416

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = [x^n] (1 + x + x^2 * (1 + x)^3)^n.

Prog

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

Crossrefs

Cf. A005725, A378405.

Sequence in context: A278089 A248016 A000269 * A370248 A370274 A015524

Adjacent sequences: A378403 A378404 A378405 * A378407 A378408 A378409

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2024

Status

approved