A381785 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)^2), where C(x) is the g.f. of A000108.

1, 2, 7, 45, 335, 2731, 23573, 211741, 1958571, 18529392, 178459000, 1743868792, 17246702932, 172302244669, 1736302280083, 17627794322287, 180133941044517, 1851310247393202, 19123511540724822, 198437973436950204, 2067524004169000212, 21620908821378509071

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A212071, A381772, A381778, A381784.

Cf. A000108.

Sequence in context: A064606 A331711 A223001 * A066612 A098637 A162045

Adjacent sequences: A381782 A381783 A381784 * A381786 A381787 A381788

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved