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

%I A246763 #19 May 22 2025 10:21:40
%S A246763 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,
%T A246763 16,73,64,2,62,69,5,29,144,16,145,157,40,9,82,75,96,88,9,100,144,36,
%U A246763 118,8,163,212,38,9,27,185,242,203,231,11,189,250,137,116,34,91,289,10,272
%N A246763 Catalan(n)^2 mod prime(n).
%H A246763 Vincenzo Librandi, <a href="/A246763/b246763.txt">Table of n, a(n) for n = 1..10000</a>
%p A246763 seq(binomial(2*n,n)^2/(n+1)^2 mod ithprime(n), n=1..100); # _Robert Israel_, Sep 03 2014
%t A246763 Table[Mod[CatalanNumber[n]^2, Prime[n]], {n, 70}]
%o A246763 (Magma) [Catalan(n)^2 mod NthPrime(n): n in [1..70]];
%o A246763 (Python)
%o A246763 from sympy import prime
%o A246763 from gmpy2 import divexact, t_mod
%o A246763 A246763, c = [1], 1
%o A246763 for n in range(2,10**2):
%o A246763     c = divexact(c*(4*n-2),(n+1))
%o A246763     A246763.append(t_mod(c**2,prime(n))) # _Chai Wah Wu_, Sep 04 2014
%Y A246763 Cf. A000040, A000108, A246714.
%K A246763 nonn
%O A246763 1,5
%A A246763 _Vincenzo Librandi_, Sep 03 2014