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A188333 T(n,k)=Number of nondecreasing arrangements of n nonzero numbers in -(n+k-2)..(n+k-2) with sum zero.

%I A188333 #7 Jul 22 2025 11:08:22
%S A188333 0,0,1,0,2,2,0,3,4,10,0,4,8,20,40,0,5,12,37,86,197,0,6,18,61,166,424,
%T A188333 980,0,7,24,94,288,828,2128,5142,0,8,32,136,472,1488,4238,11200,27632,
%U A188333 0,9,40,191,726,2519,7836,22563,60372,152191,0,10,50,257,1076,4050,13694,42593
%N A188333 T(n,k)=Number of nondecreasing arrangements of n nonzero numbers in -(n+k-2)..(n+k-2) with sum zero.
%C A188333 Table starts
%C A188333 ......0......0......0.......0.......0.......0.......0........0........0
%C A188333 ......1......2......3.......4.......5.......6.......7........8........9
%C A188333 ......2......4......8......12......18......24......32.......40.......50
%C A188333 .....10.....20.....37......61......94.....136.....191......257......338
%C A188333 .....40.....86....166.....288.....472.....726....1076.....1534.....2130
%C A188333 ....197....424....828....1488....2519....4050....6252.....9314....13479
%C A188333 ....980...2128...4238....7836...13694...22786...36454....56314....84496
%C A188333 ...5142..11200..22563...42593...76251..130453..214784...341988...528926
%C A188333 ..27632..60372.122986..236130..431488..755434.1274786..2082546..3306612
%C A188333 .152191.333254.684809.1333130.2477726.4423012.7621670.12729304.20676601
%H A188333 R. H. Hardin, <a href="/A188333/b188333.txt">Table of n, a(n) for n = 1..430</a>
%e A188333 Some solutions for n=8 k=6
%e A188333 .-8...-9..-12..-11..-12...-9...-9...-6..-11...-8..-12..-12..-12...-9..-11...-9
%e A188333 .-5...-7...-7...-7...-5...-6...-8...-6...-7...-7...-6..-12..-10...-6..-10...-7
%e A188333 .-1...-6....1...-4...-2...-3...-3...-6...-4...-4...-4...-1...-6...-2...-4...-1
%e A188333 .-1....1....1...-4...-2...-3....3...-5...-4....1...-4....2....4....1...-4...-1
%e A188333 .-1....1....2....3...-2....2....3...-5....5....1....1....4....4....1....4....1
%e A188333 ..3....2....3....6....4....4....3....5....6....3....2....4....5....3....6....5
%e A188333 ..3....9....5....8....8....7....4...11....6....4...11....4....6....5....9....6
%e A188333 .10....9....7....9...11....8....7...12....9...10...12...11....9....7...10....6
%Y A188333 Row 3 is A007590(n+1)
%K A188333 nonn,tabl
%O A188333 1,5
%A A188333 _R. H. Hardin_ Mar 28 2011