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A278627 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

%I A278627 #4 Nov 24 2016 08:46:57
%S A278627 0,3,3,16,46,16,51,357,357,51,126,1952,4754,1952,126,266,8518,49503,
%T A278627 49503,8518,266,504,31605,439446,1069536,439446,31605,504,882,103546,
%U A278627 3438414,21121532,21121532,3438414,103546,882,1452,307087,24103803
%N A278627 T(n,k)=Number of nXk 0..2 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.
%C A278627 Table starts
%C A278627 ....0......3........16............51..............126.................266
%C A278627 ....3.....46.......357..........1952.............8518...............31605
%C A278627 ...16....357......4754.........49503...........439446.............3438414
%C A278627 ...51...1952.....49503.......1069536.........21121532...........387542112
%C A278627 ..126...8518....439446......21121532........978005050.........43853346948
%C A278627 ..266..31605...3438414.....387542112......43853346948.......4902306226424
%C A278627 ..504.103546..24103803....6594175430....1892563134910.....540194658701142
%C A278627 ..882.307087.153073965..103536313036...77595353266488...58237100230743229
%C A278627 .1452.838936.888863183.1496475492375.2984253200734849.6049936223396297740
%H A278627 R. H. Hardin, <a href="/A278627/b278627.txt">Table of n, a(n) for n = 1..127</a>
%F A278627 Empirical for column k:
%F A278627 k=1: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 - (1/8)*n^2 - (13/60)*n
%F A278627 k=2: [polynomial of degree 15]
%F A278627 k=3: [polynomial of degree 43]
%F A278627 k=4: [polynomial of degree 125]
%e A278627 Some solutions for n=3 k=4
%e A278627 ..1..1..0..0. .2..2..1..1. .1..1..1..0. .2..1..0..0. .1..2..1..1
%e A278627 ..1..0..1..0. .1..1..2..2. .2..2..2..1. .2..1..1..0. .1..2..2..0
%e A278627 ..2..1..1..2. .2..0..2..2. .2..1..0..1. .0..0..2..2. .2..1..0..1
%Y A278627 Column 1 is A000574(n+1).
%K A278627 nonn,tabl
%O A278627 1,2
%A A278627 _R. H. Hardin_, Nov 24 2016