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A342288
a(n) = C(n)*C(n+2), where C(n) is the n-th Catalan number A000108(n).
2
2, 5, 28, 210, 1848, 18018, 188760, 2085798, 24018280, 285817532, 3493769552, 43672119400, 556315613280, 7202300350500, 94561966954800, 1256886144107550, 16888191533829000, 229116465142280100, 3135277944052254000, 43238333101156993800, 600502564063273528800
OFFSET
0,1
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2021
STATUS
approved