A067770 a(n) = Catalan(n) mod (n+2).

1, 1, 2, 0, 2, 0, 4, 6, 0, 0, 8, 0, 0, 10, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 20, 0, 16, 22, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 56, 0, 0, 58, 0, 0

Offset: 0

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Feb 05 2002

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000108, A059288.

Programs

Maple

a:= n-> binomial(2*n, n)/(n+1) mod (n+2):
seq(a(n), n=0..88);

Mathematica

Table[Mod[CatalanNumber[n],n+2],{n,0,90}] (* Harvey P. Dale, Mar 06 2025 *)

PARI

for(k=0,80,print1(binomial(2*k,k)/(k+1)%(k+2),", ")) \\ Hugo Pfoertner, Jul 16 2020

Python

A067770_list, c = [1,1], 1
for n in range(2,10001):
    c = c*(4*n-2)//(n+1)
    A067770_list.append(c % (n+2)) # Chai Wah Wu, Jul 16 2020

Extensions

Name corrected by Hugo Pfoertner, Jul 16 2020