A222051 - OEIS

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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

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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)}