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%I #5 Mar 31 2012 12:36:56
%S 2,3,3,4,6,4,5,12,10,5,6,21,28,15,6,7,35,69,57,21,7,8,54,154,188,104,
%T 28,8,9,80,310,544,444,176,36,9,10,113,580,1380,1614,944,280,45,10,11,
%U 155,1013,3172,5036,4206,1844,425,55,11,12,206,1680,6687,13934,15798,9880
%N T(n,k)=Number of arrays of 2n nondecreasing integers in -k..k with sum zero and equal numbers greater than zero and less than zero
%C Table starts
%C ..2..3...4....5.....6......7.......8........9.......10........11........12
%C ..3..6..12...21....35.....54......80......113......155.......206.......268
%C ..4.10..28...69...154....310.....580.....1013.....1680......2662......4064
%C ..5.15..57..188...544...1380....3172.....6687....13163.....24435.....43195
%C ..6.21.104..444..1614...5036...13934....34847....80258....172405....349182
%C ..7.28.176..944..4206..15798...51768...151393...403131....991692...2280620
%C ..8.36.280.1844..9880..43958..168314...568933..1734054...4842044..12545910
%C ..9.45.425.3369.21363.111053..491187..1899856..6570506..20665432..59915342
%C .10.55.620.5825.43136.259023.1310474..5750208.22393894..78796188.254083954
%C .11.66.876.9621.82267.565010.3241912.16015498.69763326.272964800.973625950
%H R. H. Hardin, <a href="/A203291/b203291.txt">Table of n, a(n) for n = 1..1921</a>
%e Some solutions for n=3 k=3
%e .-2...-3...-3...-1...-2...-3...-1...-3...-3...-2...-3...-3...-2...-2...-2...-3
%e .-2...-2...-2...-1....0...-3....0...-2...-2...-1...-1...-1...-2...-2...-2...-1
%e ..0...-1...-2...-1....0...-1....0...-2....0...-1...-1...-1...-1...-1...-2....0
%e ..0....1....1....1....0....2....0....2....0....1....1....1....1....1....2....0
%e ..2....2....3....1....0....2....0....2....2....1....2....1....2....1....2....2
%e ..2....3....3....1....2....3....1....3....3....2....2....3....2....3....2....2
%Y Column 2 is A000217(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Dec 31 2011
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