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

Author

Paul D. Hanna, Feb 06 2013

Keywords

• nonn

Crossrefs

Cf. A220178, A222050, A222052.

Programs

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), ", "))

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.