%I #5 Feb 06 2013 20:07:03

%S 1,6,150,4200,131670,4360356,149885736,5287716720,190170736470,

%T 6941694002100,256393942704900,9561265547652000,359399657792284200,

%U 13600394660797333200,517621830467456905200,19798076590576557847200,760517744810283004728150,29325625363665142395552900

%N Central terms in rows of triangle A220178.

%F 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).

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

%o (PARI) /* As Central Terms in Rows of Triangle A220178: */

%o {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)}

%o {a(n)=A220178(2*n, n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A220178, A222050, A222052.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 06 2013