%I
%S 2,19,712,87685,31102080,28757840751
%N Number of monotonic matrices of order n.
%C A monotonic matrix of order n is an n × N matrix in which every element is either 0 or contains a number from the set {1, 2, ..., n} subject to 3 conditions:
%C the filledin entries in each row are strictly increasing;
%C the filledin entries in each column are strictly decreasing;
%C for two filledin cells with same entry, the one further right is higher (the positive slope condition).
%C See A070214 for more information.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MonotonicMatrix.html">Monotonic Matrix</a>
%Y Cf. A070214.
%K nonn,more
%O 1,1
%A _Eric W. Weisstein_, Jul 25 2003
%E a(4) from _Rob Pratt_, Aug 23 2003
%E a(5)a(6) from _Giovanni Resta_, Jul 28 2015
