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%I #8 Jul 17 2024 18:53:05
%S 1,1,2,6,24,120,720,5040,40320,362878,3627778,39830282,475089392,
%T 6094561180,83333937940,1205398303180,18331873363480,291706615484450,
%U 4838414115229430,83404373736108502,1490681666580459304,27572241018065482032,526959942343051879032
%N Number of permutations of {1..n} with fewer than 7 interior elements having values lying between the values of their neighbors.
%H Alois P. Heinz, <a href="/A226440/b226440.txt">Table of n, a(n) for n = 0..480</a> (terms n = 1..206 from R. H. Hardin)
%e Some solutions for n=7
%e ..2....2....2....1....7....2....6....4....2....2....7....1....1....4....6....4
%e ..5....3....1....7....4....3....7....2....1....7....3....3....5....3....3....5
%e ..3....7....6....2....5....6....2....1....5....6....5....4....4....2....2....6
%e ..4....1....4....4....2....7....1....5....6....4....6....6....7....1....4....2
%e ..7....4....3....3....3....4....4....3....4....5....2....7....3....5....7....3
%e ..1....6....5....5....6....1....5....6....3....3....1....2....2....6....1....7
%e ..6....5....7....6....1....5....3....7....7....1....4....5....6....7....5....1
%Y Column 7 of A226441.
%K nonn
%O 0,3
%A _R. H. Hardin_, Jun 06 2013
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 17 2024