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Number of 3 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,6,n can be permuted, see formula.
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%I #3 Oct 03 2013 09:33:11

%S 1,84,2520,41580,457380,3737448,24293412,131589315,614083470,

%T 2530768240,9386849472,31803696288,99604982880,291153026880,

%U 800670823920,2085276513474,5172303508911,12276881393700,27999904933000,61578738292500,130994770549500,270273795363000

%N Number of 3 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,6,n can be permuted, see formula.

%F (empirical) set p,q,r to n,6,3 (in any order) in s=p+q+r-1; a(n) = product {i in 0..r-1} (binomial(s,p+i)*i!/(s-i)^(r-i-1))

%K nonn

%O 0,2

%A _R. H. Hardin_, Jul 05 2008