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%I #9 Oct 03 2025 08:25:35
%S 1,14,106,850,7074,59910,514168,4453946,38855488,341052122,3006680636,
%T 26619825378,236386648574,2105717447626,18798362729604,
%U 168222072625668,1507848061916274,13541292792666004,121763260320351938
%N Number of -7..7 arrays x(0..n-1) of n elements with zero sum and elements alternately strictly increasing and strictly decreasing.
%C Column 7 of A200057
%H R. H. Hardin, <a href="/A200056/b200056.txt">Table of n, a(n) for n = 1..189</a>
%e Some solutions for n=6
%e ..1....3....1...-6...-5....4...-1....2...-1...-5....6...-3....0...-6....6....1
%e ..5...-4....3....4...-6....5....4...-4....2....6...-1...-1...-4....7...-3....2
%e .-2...-1....2...-6....4...-5...-5...-1...-3...-4....1...-5....7...-7....7...-3
%e ..7...-5....5....1...-1....0....0...-2....3....4...-7....5...-5....0...-3....5
%e .-7....6...-7....0....6...-3...-3....5...-4...-7....4....0....5...-1....0...-7
%e .-4....1...-4....7....2...-1....5....0....3....6...-3....4...-3....7...-7....2
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 13 2011