A222051 Central terms in rows of triangle A220178.

1, 6, 150, 4200, 131670, 4360356, 149885736, 5287716720, 190170736470, 6941694002100, 256393942704900, 9561265547652000, 359399657792284200, 13600394660797333200, 517621830467456905200, 19798076590576557847200, 760517744810283004728150, 29325625363665142395552900

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (2*n+1)*binomial(2*n,n)*A222050(n), where the g.f. G(x) of A222050 satisfies: G(x) = sqrt(1 + 2*x*G(x)^4 + 3*x^2*G(x)^6).

a(n) = [x^n] d^(2*n)/dx^(2*n) (1+x+x^2)^(2*n) / (2*n)!, by definition.

Prog

(PARI) /* As Central Terms in Rows of Triangle A220178: */
{A220178(n, k)=polcoeff(polcoeff(1/sqrt(1-2*x-3*x^2 - 4*x*y +x*O(x^n)+y*O(y^k)), n, x), k, y)}
{a(n)=A220178(2*n, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A220178, A222050, A222052.

Sequence in context: A291110 A246214 A065946 * A285747 A013296 A013301

Adjacent sequences: A222048 A222049 A222050 * A222052 A222053 A222054

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2013

Status

approved