A379383 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^3) ).

1, 2, 10, 80, 750, 7680, 83252, 939008, 10905942, 129548288, 1566565452, 19220267008, 238662840780, 2993651974144, 37876206019560, 482802294325248, 6194365014836582, 79930063134392320, 1036640587694252380, 13505632613590630400, 176673045664669396132, 2319654465118014537728

Offset

0,2

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A138020, A379382.

Cf. A078531, A379328, A379331.

Sequence in context: A368951 A108486 A152168 * A003578 A274276 A152600

Adjacent sequences: A379378 A379380 A379382 * A379385 A379386 A379387

Keyword

nonn,new

Author

Seiichi Manyama, Dec 22 2024

Status

approved