A246763 Catalan(n)^2 mod prime(n).

1, 1, 0, 0, 4, 4, 16, 6, 12, 25, 7, 4, 31, 15, 8, 11, 7, 41, 23, 45, 69, 72, 29, 11, 2, 85, 4, 16, 73, 64, 2, 62, 69, 5, 29, 144, 16, 145, 157, 40, 9, 82, 75, 96, 88, 9, 100, 144, 36, 118, 8, 163, 212, 38, 9, 27, 185, 242, 203, 231, 11, 189, 250, 137, 116, 34, 91, 289, 10, 272

Offset: 1

Author

Vincenzo Librandi, Sep 03 2014

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000108, A246714.

Programs

Magma

[Catalan(n)^2 mod NthPrime(n): n in [1..70]];

Maple

seq(binomial(2*n,n)^2/(n+1)^2 mod ithprime(n), n=1..100); # Robert Israel, Sep 03 2014

Mathematica

Table[Mod[CatalanNumber[n]^2, Prime[n]], {n, 70}]

Python

from sympy import prime
from gmpy2 import divexact, t_mod
A246763, c = [1], 1
for n in range(2,10**2):
    c = divexact(c*(4*n-2),(n+1))
    A246763.append(t_mod(c**2,prime(n))) # Chai Wah Wu, Sep 04 2014