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%I #4 Feb 03 2013 09:28:34
%S 120,3853,78376,1227685,16011558,180224522,1788225862,15883318341,
%T 127864299298,942615276569,6419292213136,40684542916124,
%U 241500003506194,1349966084204199,7140088927351586,35880243705890673,171932038247810370
%N Number of nX5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order
%C Column 5 of A222005
%H R. H. Hardin, <a href="/A222003/b222003.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 66*a(n-1) -2145*a(n-2) +45760*a(n-3) -720720*a(n-4) +8936928*a(n-5) -90858768*a(n-6) +778789440*a(n-7) -5743572120*a(n-8) +37014131440*a(n-9) -210980549208*a(n-10) +1074082795968*a(n-11) -4922879481520*a(n-12) +20448884000160*a(n-13) -77413632286320*a(n-14) +268367258592576*a(n-15) -855420636763836*a(n-16) +2515943049305400*a(n-17) -6848956078664700*a(n-18) +17302625882942400*a(n-19) -40661170824914640*a(n-20) +89067326568860640*a(n-21) -182183167981760400*a(n-22) +348524321356411200*a(n-23) -624439409096903400*a(n-24) +1049058207282797712*a(n-25) -1654284096099796392*a(n-26) +2450791253481179840*a(n-27) -3413602103063071920*a(n-28) +4472995859186094240*a(n-29) -5516694892996182896*a(n-30) +6406484391866534976*a(n-31) -7007092303604022630*a(n-32) +7219428434016265740*a(n-33) -7007092303604022630*a(n-34) +6406484391866534976*a(n-35) -5516694892996182896*a(n-36) +4472995859186094240*a(n-37) -3413602103063071920*a(n-38) +2450791253481179840*a(n-39) -1654284096099796392*a(n-40) +1049058207282797712*a(n-41) -624439409096903400*a(n-42) +348524321356411200*a(n-43) -182183167981760400*a(n-44) +89067326568860640*a(n-45) -40661170824914640*a(n-46) +17302625882942400*a(n-47) -6848956078664700*a(n-48) +2515943049305400*a(n-49) -855420636763836*a(n-50) +268367258592576*a(n-51) -77413632286320*a(n-52) +20448884000160*a(n-53) -4922879481520*a(n-54) +1074082795968*a(n-55) -210980549208*a(n-56) +37014131440*a(n-57) -5743572120*a(n-58) +778789440*a(n-59) -90858768*a(n-60) +8936928*a(n-61) -720720*a(n-62) +45760*a(n-63) -2145*a(n-64) +66*a(n-65) -a(n-66)
%e Some solutions for n=3
%e ..4..2..3..5..1....2..1..3..5..4....4..2..1..3..5....4..2..3..5..1
%e ..3..5..2..4..1....1..4..3..2..5....4..1..2..5..3....3..1..5..2..4
%e ..1..5..4..3..2....1..4..3..2..5....2..1..4..5..3....1..3..2..5..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Feb 03 2013
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