A376547 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)*A(x)^3.

1, 0, 0, 1, 1, 0, 3, 6, 3, 12, 36, 36, 67, 220, 330, 493, 1420, 2730, 4158, 9933, 21693, 36312, 75684, 171360, 316011, 617424, 1374156, 2723667, 5256237, 11303028, 23362779, 45734304, 95506488, 200821140, 401891490, 825565455, 1739179533, 3549322296

Offset

0,7

Links

Table of n, a(n) for n=0..37.

Formula

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

Prog

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

Crossrefs

Cf. A017817, A366588, A376486.

Sequence in context: A109044 A205844 A205865 * A362585 A085881 A265480

Adjacent sequences: A376544 A376545 A376546 * A376548 A376549 A376550

Keyword

nonn

Author

Seiichi Manyama, Sep 27 2024

Status

approved