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A278727 T(n,k)=Number of nXk 0..3 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.

%I A278727 #4 Nov 27 2016 06:51:35
%S A278727 4,10,10,20,60,20,35,275,275,35,56,1050,3232,1050,56,84,3492,33466,
%T A278727 33466,3492,84,120,10401,306070,1058494,306070,10401,120,165,28288,
%U A278727 2487889,30942600,30942600,2487889,28288,165,220,71266,18151220,815294800
%N A278727 T(n,k)=Number of nXk 0..3 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order.
%C A278727 Table starts
%C A278727 ...4.....10........20............35.................56.....................84
%C A278727 ..10.....60.......275..........1050...............3492..................10401
%C A278727 ..20....275......3232.........33466.............306070................2487889
%C A278727 ..35...1050.....33466.......1058494...........30942600..............815294800
%C A278727 ..56...3492....306070......30942600.........3062815568...........279368748599
%C A278727 ..84..10401...2487889.....815294800.......279368748599.........90462380211862
%C A278727 .120..28288..18151220...19328645044.....23161560633508......26947618206791521
%C A278727 .165..71266.120104810..414671691083...1747727428639023....7361981179311574929
%C A278727 .220.168155.727684612.8109321869307.120668752462156921.1850980180963910285369
%H A278727 R. H. Hardin, <a href="/A278727/b278727.txt">Table of n, a(n) for n = 1..111</a>
%F A278727 Empirical for column k:
%F A278727 k=1: a(n) = (1/6)*n^3 + 1*n^2 + (11/6)*n + 1
%F A278727 k=2: [polynomial of degree 12]
%F A278727 k=3: [polynomial of degree 45]
%e A278727 Some solutions for n=3 k=4
%e A278727 ..1..1..1..0. .2..2..0..0. .2..1..1..0. .3..1..1..0. .2..1..1..0
%e A278727 ..2..1..1..1. .3..0..3..0. .2..1..1..2. .3..2..2..2. .2..2..1..0
%e A278727 ..3..2..1..1. .3..1..3..2. .2..2..0..1. .3..3..2..3. .3..1..3..0
%Y A278727 Column 1 is A000292(n+1).
%Y A278727 Diagonal is A229771.
%K A278727 nonn,tabl
%O A278727 1,1
%A A278727 _R. H. Hardin_, Nov 27 2016