A277584 - OEIS

%I #23 Sep 08 2022 08:46:17

%S 0,1,25,784,27225,1002001,38291344,1502337600,60101954649,

%T 2440703175625,100300325150025,4161829109817600,174077451630810000,

%U 7330421677037621904,310467090932230849600,13214837914326197526784,564927069263895118093401

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

%H Seiichi Manyama, <a href="/A277584/b277584.txt">Table of n, a(n) for n = 0..605</a>

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

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

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

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

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

%o (PARI) a(n) = binomial(3*n-1, n-1)^2; \\ _Michel Marcus_, Oct 22 2016

%o (Magma) [Binomial(3*n-1, n-1)^2: n in [0..20]]; // _Vincenzo Librandi_, Oct 23 2016

%Y Cf. A025174, A060150, A188662.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 22 2016