%I #12 May 17 2020 01:40:51
%S 1,1,3,19,391,25532,5539434,4116290300,10699755803977,
%T 98834805799836193,3285452504354615242708,397045217438108647483964418,
%U 175907525023476787251523714204914,287726899459800056272961335544498108972,1747931723877860528675045077016711589788124993
%N Number of lower triangles of an n X n 0..n array with all row sums equal to the length of the row and all column sums equal to the length of the column.
%e Some solutions for n=4:
%e ..1........1........1........1........1........1........1........1
%e ..2.0......0.2......2.0......0.2......2.0......1.1......1.1......2.0
%e ..1.1.1....1.1.1....0.2.1....2.1.0....1.2.0....0.2.1....2.1.0....1.0.2
%e ..0.2.1.1..2.0.1.1..1.1.1.1..1.0.2.1..0.1.2.1..2.0.1.1..0.1.2.1..0.3.0.1
%Y Diagonal of A195644.
%K nonn
%O 1,3
%A _R. H. Hardin_, Sep 21 2011
%E a(12)-a(15) from _Andrew Howroyd_, May 16 2020