A371496 G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^4.

1, 4, 22, 156, 1233, 10420, 92120, 841376, 7876616, 75177492, 728784802, 7156081536, 71024862452, 711383912672, 7181295333306, 72989746391780, 746308443708928, 7671359593228624, 79226966456758424, 821691132077059740, 8554576791134761387

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(5*k+3,k)/(k+1).

G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349361.

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(5*k+3, k)/(k+1));

Crossrefs

Cf. A001006, A371494, A371495.

Cf. A118971, A349361.

Sequence in context: A302548 A052772 A365124 * A052650 A198053 A197925

Adjacent sequences: A371493 A371494 A371495 * A371497 A371498 A371499

Keyword

nonn

Author

Seiichi Manyama, Mar 25 2024

Status

approved