A172668 Number of 3*n X n 0..2 arrays with row sums 2 and column sums 6.

1, 141, 352128, 6152037276, 467046072593100, 115428185943399529200, 76497104228450459248094400, 118274738663434470504494036529600, 384184227197088213207839624049360408000, 2415977451999318332950627138384873223959560000

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..33

Formula

a(n) = 720^(-n)*n!(3n)! Sum_{i=0..n} Sum_{j=0..n-i} Sum_{k=0..n-i-j} (15^(n-i-k)*45^k*(6i+4j+2k)!/(i!j!k!(n-i-j-k)!(2j+k+3i)!*2^(2j+k+3i))). - Shanzhen Gao, Feb 24 2010

a(n) ~ sqrt(Pi) * 3^(4*n + 1/2) * n^(6*n + 1/2) / (2^(n-1) * 5^n * exp(6*n - 5/2)). - Vaclav Kotesovec, Oct 22 2023

Mathematica

Table[720^(-n)*n!*(3*n)! * Sum[Sum[Sum[(15^(n-i-k)*45^k*(6*i+4*j+2*k)! / (i!*j!*k!*(n-i-j-k)!*(2*j+k+3*i)! * 2^(2*j+k+3*i))), {k, 0, n-i-j}], {j, 0, n-i}], {i, 0, n}], {n, 1, 15}] (* Vaclav Kotesovec, Oct 22 2023 *)

Prog

(PARI) a(n) = 720^(-n)*n!*(3*n)!*sum(i=0, n, sum(j=0, n-i, sum(k=0, n-i-j, (15^(n-i-k)*45^k*(6*i+4*j+2*k)!/(i!*j!*k!*(n-i-j-k)!*(2*j+k+3*i)!*2^(2*j+k+3*i)))))) \\ Michel Marcus, Jan 17 2018

Crossrefs

Sequence in context: A164525 A153358 A066627 * A172764 A172836 A087001

Adjacent sequences: A172665 A172666 A172667 * A172669 A172670 A172671

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved