A378463 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-k-1,n-3*k).

1, 1, 3, 13, 59, 266, 1203, 5489, 25259, 117022, 545038, 2549592, 11970035, 56372460, 266194295, 1259910113, 5975382699, 28390616727, 135108035502, 643891031826, 3072604703774, 14679493913048, 70206875750168, 336103001918788, 1610476039036259, 7723148579525441

Offset

0,3

Links

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

Formula

a(n) = [x^n] 1/(1 - x - x^3/(1 - x))^n.

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-k-1, n-3*k));

Crossrefs

Cf. A370624, A378464.

Cf. A054515.

Sequence in context: A336791 A268596 A199297 * A152594 A052984 A360143

Adjacent sequences: A378460 A378461 A378462 * A378464 A378465 A378466

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2024

Status

approved