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A221620 Number of n X 5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row.

%I A221620 #8 Aug 09 2018 15:24:14
%S A221620 120,10055,738150,51149685,3451956516,230141263315,15258126049410,
%T A221620 1009051056050225,66655625407012320,4400938611593606031,
%U A221620 290509268912775739710,19174945298440265379565,1265583745617128902739100
%N A221620 Number of n X 5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row.
%C A221620 Column 5 of A221623.
%H A221620 R. H. Hardin, <a href="/A221620/b221620.txt">Table of n, a(n) for n = 1..210</a>
%F A221620 Empirical: a(n) = 120*a(n-1) - 4345*a(n-2) + 52950*a(n-3) - 93340*a(n-4) + 44616*a(n-5).
%F A221620 Empirical g.f.: x*(120 - 4345*x + 52950*x^2 - 93340*x^3 + 44616*x^4) / ((1 - x)^2*(1 - 26*x)^2*(1 - 66*x)). - _Colin Barker_, Aug 09 2018
%e A221620 Some solutions for n=3:
%e A221620 ..1..2..3..4..5....1..2..4..3..5....1..2..4..3..5....1..2..3..5..4
%e A221620 ..4..5..1..3..2....1..2..5..4..3....4..3..1..2..5....1..2..5..3..4
%e A221620 ..5..1..2..4..3....3..5..4..1..2....5..3..4..1..2....1..3..4..5..2
%Y A221620 Cf. A221623.
%K A221620 nonn
%O A221620 1,1
%A A221620 _R. H. Hardin_, Jan 21 2013