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A212943 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows.

%I A212943 #6 Jul 22 2025 23:00:38
%S A212943 1,1,1,1,7,1,1,181,37,1,1,10311,9019,175,1,1,1016501,6470341,331489,
%T A212943 781,1,1,152747323,10058484751,2509306671,10669771,3367,1,1,
%U A212943 32383630189,28744943858947,52311221188001,801439905901,320396041,14197,1,1
%N A212943 T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows.
%C A212943 Table starts
%C A212943 .1...1........1............1..................1........................1
%C A212943 .1...7......181........10311............1016501................152747323
%C A212943 .1..37.....9019......6470341........10058484751...........28744943858947
%C A212943 .1.175...331489...2509306671.....52311221188001......2438624218076957695
%C A212943 .1.781.10669771.801439905901.212180664326328751.153322267564381742818531
%H A212943 R. H. Hardin, <a href="/A212943/b212943.txt">Table of n, a(n) for n = 1..191</a>
%F A212943 Empirical for column k:
%F A212943 k=1: a(n) = a(n-1)
%F A212943 k=2: a(n) = 7*a(n-1) -12*a(n-2)
%F A212943 k=3: a(n) = 55*a(n-1) -936*a(n-2) +4860*a(n-3)
%F A212943 k=4: a(n) = 631*a(n-1) -144700*a(n-2) +15035200*a(n-3) -702208000*a(n-4) +11468800000*a(n-5)
%F A212943 The coefficient of a(n-1) is A209668(k) (through at least k=1..7)
%e A212943 Some solutions for n=4 k=4
%e A212943 ..1..3..2..2....0..0..0..3....1..3..0..1....1..3..2..1....1..3..3..3
%e A212943 ..1..1..2..2....0..1..1..2....0..0..1..0....1..1..0..3....2..3..0..3
%e A212943 ..0..1..3..1....0..2..2..1....0..1..1..3....2..3..3..0....0..2..0..2
%e A212943 ..3..1..0..3....2..1..0..2....3..0..3..1....1..0..3..0....2..0..1..0
%Y A212943 Column 2 is A005061
%Y A212943 cf. A212930
%K A212943 nonn,tabl
%O A212943 1,5
%A A212943 _R. H. Hardin_ May 31 2012