%I
%S 2621,9459,26167,69404,188735,558151,1745634,5935728,20786804,
%T 77416352,219059475,578513498,1500419043,3908857765,10470345790,
%U 28385741484,79729201108,221303407539,630847591899,1653827513009,4173815556603,10415200154855,25901062216475
%N Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with nine.
%C An upjump j occurs at position i in p if p_{i} > p_{i1} 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_{i1}. A downjump j occurs at position i in p if p_{i} < p_{i1} 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_{i1}. First index in the lists is 1 here.
%H Alois P. Heinz, <a href="/A292175/b292175.txt">Table of n, a(n) for n = 9..2000</a>
%e a(9) = 2621: 912345678, 913245678, 913425678, 913452678, 913456278, 913456728, 913456782, 913524678, 913526478, 913526748, ..., 975846321, 975864321, 976543218, 976543281, 976543821, 976548321, 976584321, 976854321, 978654321, 987654321.
%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p add(b(uj, o+j1, j), j=1..min(t, u))+
%p add(b(u+j1, oj, j), j=1..min(t, o)))
%p end:
%p a:= n> b(0, n, 9)b(0, n, 8):
%p seq(a(n), n=9..50);
%Y Column k=9 of A291684.
%K nonn
%O 9,1
%A _Alois P. Heinz_, Sep 10 2017
