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

1,1

Comments

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

Links

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

Example

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.

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}]

Prog

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

Crossrefs

Cf. A000108, A118112, A118113.

Sequence in context: A362107 A364910 A291873 * A366555 A266067 A300368

Adjacent sequences: A118111 A118112 A118113 * A118115 A118116 A118117

Keyword

nonn

Author

Labos Elemer, Apr 13 2006

Status

approved