%I #5 Dec 18 2015 18:17:46
%S 1,1,3,19,391,25532,5539434,4116290300,10699674783969,
%T 98827025484631957,3284291571314714878300
%N Number of lower triangles of an n X n 0..7 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 7 of A194644
%e Some solutions for n=7
%e ..1..............1..............1..............1..............1
%e ..1.1............0.2............2.0............2.0............2.0
%e ..0.3.0..........0.3.0..........3.0.0..........2.1.0..........2.1.0
%e ..4.0.0.0........2.1.1.0........0.2.2.0........1.3.0.0........2.2.0.0
%e ..0.2.2.0.1......2.0.1.1.1......1.1.2.0.1......1.2.2.0.0......0.1.0.3.1
%e ..1.0.1.0.2.2....2.0.2.0.2.0....0.3.0.1.2.0....0.0.2.4.0.0....0.1.4.0.1.0
%e ..0.0.2.4.0.0.1..0.0.1.3.0.2.1..0.0.1.3.0.2.1..0.0.1.0.3.2.1..0.1.1.1.1.2.1
%K nonn
%O 1,3
%A _R. H. Hardin_ Sep 21 2011