%I #5 Dec 18 2015 18:17:46
%S 1,1,3,19,391,25532,5539434,4116036800,10694128575819,
%T 98630958757213465,3267417937114919996252
%N Number of lower triangles of an n X n 0..6 array with all row sums equal to the length of the row and all column sums equal to the length of the column
%C Column 6 of A194644
%e Some solutions for n=6
%e ..1............1............1............1............1............1
%e ..1.1..........1.1..........0.2..........2.0..........0.2..........2.0
%e ..2.1.0........2.1.0........2.1.0........2.1.0........2.1.0........2.1.0
%e ..2.0.0.2......1.2.1.0......0.0.3.1......0.2.1.1......0.1.3.0......0.3.1.0
%e ..0.0.2.1.2....1.0.2.0.2....1.0.1.1.2....0.1.2.2.0....1.0.1.1.2....1.0.2.1.1
%e ..0.3.2.0.0.1..0.1.1.3.0.1..2.2.0.1.0.1..1.1.1.0.2.1..2.1.0.2.0.1..0.1.1.2.1.1
%K nonn
%O 1,3
%A _R. H. Hardin_ Sep 21 2011