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 A356853 Number of permutations p of [2n+1] such that at most one element of {p(1),...,p(i-1)} is between p(i) and p(i+1) for all i <= 2n and p(2n+1) = n+1. 2
 1, 2, 20, 216, 2720, 36228, 503216, 7171404, 104142520, 1533200656, 22811374568, 342216338652, 5168324302672, 78483423004680, 1197266739443160, 18335055482658748, 281714880491273736, 4340894020114398672, 67055152953864109240, 1038097819961270208088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..832 FORMULA a(n) = A356692(2n,n). EXAMPLE a(0) = 1: 1. a(1) = 2: 132, 312. a(2) = 20: 12453, 12543, 14253, 14523, 15243, 15423, 21453, 21543, 25143, 25413, 41253, 41523, 45123, 45213, 51243, 51423, 52143, 52413, 54123, 54213. a(3) = 216: 1235764, 1236754, 1237564, 1237654, ..., 7651234, 7651324, 7652134, 7653124. MAPLE b:= proc(u, o) option remember; `if`(u+o=0, 1, add(b(sort([o-j, u+j-1])[]), j=1..min(2, o))+ add(b(sort([u-j, o+j-1])[]), j=1..min(2, u))) end: a:= n-> b(n\$2): seq(a(n), n=0..20); # second Maple program: b:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1, add(b(n-1, j), j=k-2..k+1))) end: a:= n-> b(2*n, n): seq(a(n), n=0..20); CROSSREFS Cf. A356692. Sequence in context: A226301 A000906 A308945 * A199761 A214769 A227337 Adjacent sequences: A356850 A356851 A356852 * A356854 A356855 A356856 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 31 2022 STATUS approved

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Last modified August 15 00:19 EDT 2024. Contains 375171 sequences. (Running on oeis4.)