A358436 - OEIS

A358436

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

1, 2, 8, 45, 322, 2730, 26004, 268554, 2940080, 33635316, 398300344, 4849845000, 60429982144, 767721774800, 9916427702880, 129937069996965, 1724052965464890, 23129299114182030, 313351935000465900, 4282621342230699930, 58994556159403576140, 818487022124443918740

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OFFSET

0,2

LINKS

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

FORMULA

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

a(n) = ((-64*n^3 + 160*n^2 - 112*n + 24)*a(n-2) + (20*n^3 - 14*n^2 + 2*n)*a(n-1)) / (n*(n + 1)^2).

MAPLE

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

A358436 := n -> add(C(n)*C(n-j), j = 0..n):

seq(A358436(n), n = 0..21);