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%I #5 Sep 10 2017 20:03:17
%S 10061,37702,107175,285492,786489,2249024,6929078,22322520,77416352,
%T 274792342,1035050705,2962838350,7926847142,20648853479,54254560137,
%U 143941539439,393399319076,1083862520072,3084318416024,8650938117110,24829005575685,65609605382112
%N Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with ten.
%C An up-jump j occurs at position i in p if p_{i} > p_{i-1} and j is the index of p_i in the increasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are larger than p_{i-1}. A down-jump j occurs at position i in p if p_{i} < p_{i-1} and j is the index of p_i in the decreasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are smaller than p_{i-1}. First index in the lists is 1 here.
%H Alois P. Heinz, <a href="/A292176/b292176.txt">Table of n, a(n) for n = 10..2000</a>
%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p add(b(u-j, o+j-1, j), j=1..min(t, u))+
%p add(b(u+j-1, o-j, j), j=1..min(t, o)))
%p end:
%p a:= n-> b(0, n, 10)-b(0, n, 9):
%p seq(a(n), n=10..50);
%Y Column k=10 of A291684.
%K nonn
%O 10,1
%A _Alois P. Heinz_, Sep 10 2017
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