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%I #8 Mar 15 2023 11:05:20
%S 720,138715,15637284,1252017597,77961426700,3982479033010,
%T 172906859984380,6543173556319109,219895864612975276,
%U 6658221038381059161,183720358904970752868,4662354960197094985853,109643129437736738271166
%N Number of n X 6 arrays with each row a permutation of 1..6 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.
%C Column 6 of A222005.
%H R. H. Hardin, <a href="/A222004/b222004.txt">Table of n, a(n) for n = 1..203</a>
%e Some solutions for n=3
%e ..4..1..2..3..5..6....1..4..6..2..5..3....4..1..2..5..6..3....1..3..5..6..2..4
%e ..1..3..5..4..6..2....1..3..6..4..2..5....1..6..3..5..2..4....1..3..2..5..4..6
%e ..1..2..6..3..5..4....1..2..5..4..3..6....1..2..5..4..3..6....1..2..4..3..6..5
%Y Cf. A222005.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 03 2013