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

3, 3, 4, 15, 21, 28, 0, 81, 55, 99, 0, 0, 84, 120, 0, 153, 171, 285, 0, 231, 253, 0, 360, 0, 0, 0, 0, 522, 0, 496, 0, 561, 833, 945, 0, 703, 741, 156, 0, 861, 903, 1419, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 1664, 2145, 2211, 3417, 0, 2415, 2485, 2556, 0

Offset: 1

Author

Labos Elemer, Apr 13 2006

Keywords

• nonn

Comments

Compared with A118112: larger nonzero value more often and in non-monotonic order.

Examples

			For n=5, binomial(15,5) = 3003 = (5+1)*(5+2)*71 + 21, a(5) = 21, the residue.
Interestingly, a very large zone of zeros occurs between about n=5460 and n=7800, uninterrupted by nonzero residues.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000108, A118112, A118113.

Programs

Maple

seq(binomial(3*n,n) mod((n+1)*(n+2)),n=1..71); # Emeric Deutsch, Apr 15 2006

Mathematica

Table[Mod[Binomial[3*k, k], (k + 1)*(k + 2)], {k, 1, 1000}]

PARI

a(n) = binomial(3*n,n) % ((n+1)*(n+2)); \\ Michel Marcus, Jan 05 2017