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A188117 Number of strictly increasing arrangements of n nonzero numbers in -(n+2)..(n+2) with sum zero.

%I A188117 #9 Jul 22 2025 11:00:00
%S A188117 0,4,8,31,90,308,1032,3528,12124,42262,148518,525869,1874648,6725266,
%T A188117 24260940,87958188,320349712,1171609968,4301272078,15846418258,
%U A188117 58569008756,217121189648,807123533172,3008133255026,11238226082080
%N A188117 Number of strictly increasing arrangements of n nonzero numbers in -(n+2)..(n+2) with sum zero.
%C A188117 Column 4 of A188122
%H A188117 R. H. Hardin, <a href="/A188117/b188117.txt">Table of n, a(n) for n = 1..29</a>
%e A188117 Some solutions for n=6
%e A188117 .-4...-7...-8...-6...-7...-8...-7...-8...-8...-5...-6...-5...-7...-8...-8...-3
%e A188117 .-3...-5...-6...-5...-3...-5...-5...-5...-6...-4...-4...-3...-6...-2...-7...-2
%e A188117 .-1...-1...-4...-3...-2...-3...-3...-3...-2...-1...-2...-2....1...-1....1...-1
%e A188117 ..1....1....5....1...-1....3....4....2....2....1....1....1....3....1....2....1
%e A188117 ..2....4....6....6....5....6....5....6....6....2....3....2....4....4....4....2
%e A188117 ..5....8....7....7....8....7....6....8....8....7....8....7....5....6....8....3
%K A188117 nonn
%O A188117 1,2
%A A188117 _R. H. Hardin_ Mar 21 2011