A342288 a(n) = C(n)*C(n+2), where C(n) is the n-th Catalan number A000108(n).

2, 5, 28, 210, 1848, 18018, 188760, 2085798, 24018280, 285817532, 3493769552, 43672119400, 556315613280, 7202300350500, 94561966954800, 1256886144107550, 16888191533829000, 229116465142280100, 3135277944052254000, 43238333101156993800, 600502564063273528800

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = a(n-1)*4*(2*n-1)*(2*n+3)/((n+1)*(n+3)). - Chai Wah Wu, Mar 26 2021

Sum_{n>=0} a(n)/4^(2*n+2) = 1/2 - 16/(15*Pi). - Amiram Eldar, Apr 02 2022

Mathematica

a[n_] := CatalanNumber[n] * CatalanNumber[n + 2]; Array[a, 21, 0] (* Amiram Eldar, Apr 02 2022 *)

Prog

(Python)
A342288_list = [2]
for n in range(1, 100): A342288_list.append(A342288_list[-1]*4*(2*n-1)*(2*n+3)//((n+1)*(n+3))) # Chai Wah Wu, Mar 26 2021

Crossrefs

Inspired by A000108, A005568, A014228.

Sequence in context: A019043 A009635 A216401 * A324264 A138293 A316972

Adjacent sequences: A342285 A342286 A342287 * A342289 A342290 A342291

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2021

Status

approved