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A358118

a(n) = Sum_{j=0..n} (-1)^j*binomial(2*n - j, j)*c(n - j + 1)^2, where c(n) is the n-th Catalan number.

1, 3, 14, 94, 728, 6220, 56960, 549412, 5517746, 57235402, 609632284, 6638455152, 73653980850, 830429715762, 9494320306104, 109882451968812, 1285515149382226, 15184272319785322, 180901975355930990, 2171974459996885630, 26260944994924397048, 319547523490735463404

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

G.f.: ((1-14*x+x^2)^(1/2)*(x+1)^2*hypergeom([-1/2, 3/2],[1],-16*x/(1-14*x+x^2))-x^3-7*x^2-7*x-1)/(4*x^2). - Mark van Hoeij, Nov 11 2022

MAPLE

c := n -> binomial(2*n, n)/(n + 1):

A358118 := n -> add((-1)^j*binomial(2*n-j, j)*c(n-j+1)^2, j = 0..n):

seq(A358118(n), n = 0..21);

PROG