A277584 a(n) = binomial(3n-1, n-1)^2.

0, 1, 25, 784, 27225, 1002001, 38291344, 1502337600, 60101954649, 2440703175625, 100300325150025, 4161829109817600, 174077451630810000, 7330421677037621904, 310467090932230849600, 13214837914326197526784, 564927069263895118093401

Offset: 0

Author

Seiichi Manyama, Oct 22 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..605

Crossrefs

Cf. A025174, A060150, A188662.

Programs

Magma

[Binomial(3*n-1, n-1)^2: n in [0..20]]; // Vincenzo Librandi, Oct 23 2016

Mathematica

Table[Boole[n > 0] Binomial[3 n - 1, n - 1]^2, {n, 0, 16}] (* Michael De Vlieger, Oct 26 2016 *)

PARI

a(n) = binomial(3*n-1, n-1)^2; \\ Michel Marcus, Oct 22 2016

Formula

a(n) = A025174(n)^2.

a(n) = A188662(n)/9 for n > 0.

Let the number of multisets of length k on n symbols be denoted by ((n, k)) = binomial(n+k-1, k).

a(n) = (Sum_{k=0..n} binomial(n, k)^2 * ((2*n, 2*n - k)))/5 for n > 0.