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

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);

Mathematica

Array[CatalanNumber[#]^2*Hypergeometric2F1[-#-1, -#, 1/2-#, -1/4] &, 25, 0] (* Paolo Xausa, Feb 19 2024 *)

Crossrefs

Cf. A000108, A358436.

Sequence in context: A191812 A059104 A094071 * A289679 A352270 A136222

Adjacent sequences: A358434 A358435 A358436 * A358438 A358439 A358440

Keyword

nonn

Author

Peter Luschny, Nov 16 2022

Status

approved