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

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);

Crossrefs

Cf. A000108, A358437.

Sequence in context: A290445 A152401 A325138 * A009345 A084553 A144164

Adjacent sequences: A358433 A358434 A358435 * A358437 A358438 A358439

Keyword

nonn

Author

Peter Luschny, Nov 16 2022

Status

approved