A254746 a(n) = Catalan(n^2) mod prime(n).

1, 2, 2, 5, 8, 0, 0, 11, 0, 24, 0, 0, 29, 0, 0, 0, 0, 39, 58, 0, 21, 33, 9, 69, 9, 0, 16, 86, 0, 0, 0, 0, 0, 64, 139, 0, 0, 0, 75, 12, 4, 0, 0, 119, 195, 0, 193, 202, 0, 0, 55, 218, 0, 0, 0, 0, 84, 201, 0, 0, 203, 275, 0, 198, 159, 0, 0, 0, 0, 255, 13, 204, 0

Offset: 1

Author

Vincenzo Librandi, Feb 07 2015

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A214441, A246714, A254706.

Programs

Magma

[Catalan(n^2) mod NthPrime(n): n in [1..100]];

Mathematica

Table[Mod[CatalanNumber[n^2], Prime[n]], {n, 80}]

Python

from sympy import factorint, prime
A254746_list, c, s, s2 = [1], {}, 2, 4
for n in range(2,10**3+1):
    for p,e in factorint(4*n-2).items():
        if p in c:
            c[p] += e
        else:
            c[p] = e
    for p,e in factorint(n+1).items():
        if c[p] == e:
            del c[p]
        else:
            c[p] -= e
    if n == s2:
        d, ps = 1, prime(s)
        for p,e in c.items():
            d = (d*pow(p,e,ps)) % ps
        A254746_list.append(d)
        s2 += 2*s+1
        s += 1 # Chai Wah Wu, Feb 14 2015

Formula

a(n) = A000108(n^2) mod A000040(n).