A358437 - OEIS

A358437

a(n) = Sum_{j=0..n} binomial(n, j)*C(n)*C(n-j), where C(n) is the n-th Catalan number.

1, 2, 10, 75, 714, 7896, 96492, 1265550, 17496050, 251958564, 3748716036, 57282665622, 895001791740, 14249639190000, 230568513719400, 3783394404776475, 62848104088770450, 1055378592304360500, 17894108081334292500, 306026774743629058350, 5274529871824080624900

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OFFSET

0,2

LINKS

Paolo Xausa, Table of n, a(n) for n = 0..750

FORMULA

a(n) = C(n)^2*hypergeom([-n - 1, -n], [1/2 - n], -1/4).

a(n) = ((-80*n^3 + 240*n^2 - 220*n + 60)*a(n-2) + (24*n^3 - 20*n^2 + 4*n)*a(n-1)) / (n*(n + 1)^2) for n >= 2.

MAPLE

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

A358437 := n -> add(binomial(n, j)*C(n)*C(n-j), j = 0..n):

seq(A358437(n), n = 0..20);