A391454 Expansion of g^2/(1 + x^3*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 51, 337, 2379, 17620, 135112, 1063645, 8546809, 69815202, 578023750, 4839738501, 40910211110, 348648196840, 2992390437879, 25842906965328, 224409469141039, 1958188706568797, 17161676257412695, 150996915954255514, 1333269446351120464

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (k+2) * binomial(4*n-11*k+2,n-3*k)/(4*n-11*k+2).

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(k+2)*binomial(4*n-11*k+2, n-3*k)/(4*n-11*k+2));

Crossrefs

Cf. A002293, A389653.

Sequence in context: A246464 A391458 A391456 * A355397 A009310 A091319

Adjacent sequences: A391451 A391452 A391453 * A391455 A391456 A391457

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved