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%I #5 Mar 31 2012 12:36:11
%S 1,1,2,1,3,5,1,4,8,18,1,5,13,33,73,1,6,18,55,141,338,1,7,25,86,252,
%T 676,1656,1,8,32,126,414,1242,3370,8512,1,9,41,177,649,2137,6375,
%U 17575,45207,1,10,50,241,967,3486,11322,33885,94257,246448,1,11,61,318,1394,5444
%N T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero
%C Table starts
%C ......1......1.......1.......1.......1.......1........1........1........1
%C ......2......3.......4.......5.......6.......7........8........9.......10
%C ......5......8......13......18......25......32.......41.......50.......61
%C .....18.....33......55......86.....126.....177......241......318......410
%C .....73....141.....252.....414.....649.....967.....1394.....1944.....2649
%C ....338....676....1242....2137....3486....5444.....8196....11963....17002
%C ...1656...3370....6375...11322...19138...30982....48417....73316...108108
%C ...8512..17575...33885...61731..107233..178870...288100...450096...684572
%C ..45207..94257..184717..343363..610358.1043534..1724882..2767118..4323349
%C .246448.517971.1028172.1943488.3521260.6147894.10388788.17052653.27273240
%H R. H. Hardin, <a href="/A188211/b188211.txt">Table of n, a(n) for n = 1..430</a>
%e Some solutions for n=5 k=3
%e .-5...-5...-4...-4...-6...-3...-6...-4...-2...-6...-2...-6...-4...-5...-5...-4
%e .-2...-1...-4...-2...-5...-3...-1...-3...-1...-6...-1...-1...-3...-4...-3...-4
%e ..0....0...-1...-2...-1...-1....0...-1...-1....1...-1....0....1...-1....0....1
%e ..1....0....3....3....6....2....2....3....1....5....0....1....1....5....4....3
%e ..6....6....6....5....6....5....5....5....3....6....4....6....5....5....4....4
%Y Column 1 is A039744
%Y Column 2 is A109655
%Y Row 3 is A000982(n+2)
%Y Row 5 is A188183(n+2)
%Y Row 7 is A188185(n+3)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Mar 24 2011
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