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%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
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