cp's OEIS Frontend

A118114 a(n) = binomial(3n,n) mod((n+1)(n+2)).

%I A118114 #12 Jan 05 2017 16:14:57
%S A118114 3,3,4,15,21,28,0,81,55,99,0,0,84,120,0,153,171,285,0,231,253,0,360,0,
%T A118114 0,0,0,522,0,496,0,561,833,945,0,703,741,156,0,861,903,1419,0,0,0,0,0,
%U A118114 0,0,0,0,0,0,0,0,0,0,0,0,0,0,2016,1664,2145,2211,3417,0,2415,2485,2556,0
%N A118114 a(n) = binomial(3n,n) mod((n+1)(n+2)).
%C A118114 Compared with A118112: larger nonzero value more often and in non-monotonic order.
%H A118114 Michel Marcus, <a href="/A118114/b118114.txt">Table of n, a(n) for n = 1..10000</a>
%e A118114 For n=5, binomial(15,5) = 3003 = (5+1)*(5+2)*71 + 21, a(5) = 21, the residue.
%e A118114 Interestingly, a very large zone of zeros occurs between about n=5460 and n=7800, uninterrupted by nonzero residues.
%p A118114 seq(binomial(3*n,n) mod((n+1)*(n+2)),n=1..71); # _Emeric Deutsch_, Apr 15 2006
%t A118114 Table[Mod[Binomial[3*k, k], (k + 1)*(k + 2)], {k, 1, 1000}]
%o A118114 (PARI) a(n) = binomial(3*n,n) % ((n+1)*(n+2)); \\ _Michel Marcus_, Jan 05 2017
%Y A118114 Cf. A000108, A118112, A118113.
%K A118114 nonn
%O A118114 1,1
%A A118114 _Labos Elemer_, Apr 13 2006