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A221622 Number of nX7 arrays with each row a permutation of 1..7 having at least as many downsteps as the preceding row.

%I A221622 #6 Jul 23 2025 02:03:39
%S A221622 5040,17052210,49096652080,130516916069715,332469512259607296,
%T A221622 827196295133181978340,2031241364747667201263520,
%U A221622 4951481629224145844957738085,12021159412525485182456506260880
%N A221622 Number of nX7 arrays with each row a permutation of 1..7 having at least as many downsteps as the preceding row.
%C A221622 Column 7 of A221623
%H A221622 R. H. Hardin, <a href="/A221622/b221622.txt">Table of n, a(n) for n = 1..210</a>
%F A221622 Empirical: a(n) = 5040*a(n-1) -8349390*a(n-2) +5234439280*a(n-3) -936232732785*a(n-4) +51206316902496*a(n-5) -99624831647040*a(n-6) +49349521382400*a(n-7)
%e A221622 Some solutions for n=3
%e A221622 ..1..4..2..3..5..6..7....1..4..2..3..5..6..7....1..4..2..3..5..6..7
%e A221622 ..2..1..3..7..6..4..5....2..1..3..5..4..6..7....2..1..3..6..7..5..4
%e A221622 ..3..6..5..7..2..1..4....2..1..3..5..7..4..6....6..2..5..4..3..7..1
%K A221622 nonn
%O A221622 1,1
%A A221622 _R. H. Hardin_ Jan 21 2013