A379038 G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(4/3)) )^3.

1, 6, 39, 320, 2907, 28152, 284907, 2977116, 31875708, 347884085, 3855802689, 43283239650, 491083601338, 5622489637407, 64877058557079, 753705528179424, 8808460811302728, 103487549564845200, 1221565052783161763, 14480208437556590346, 172299129911222223324

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A364337.

a(n) = 3 * Sum_{k=0..n} binomial(4*k+3,k) * binomial(4*k+3,n-k)/(4*k+3).

Prog

(PARI) a(n) = 3*sum(k=0, n, binomial(4*k+3, k)*binomial(4*k+3, n-k)/(4*k+3));

Crossrefs

Cf. A364337, A379039.

Sequence in context: A067273 A187117 A137972 * A007322 A341728 A058191

Adjacent sequences: A379035 A379036 A379037 * A379039 A379040 A379041

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2024

Status

approved