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A321116 Number of permutations p of [n] such that in 0p the largest up-jump equals nine xx and no down-jump is larger than 2.

%I A321116 #5 Oct 27 2018 16:24:56
%S A321116 672,5454,40272,283688,1948408,13188482,88469166,589852620,3914957358,
%T A321116 25886899652,170722453774,1123938295984,7390061858416,48546948619410,
%U A321116 318711158282218,2091405520367970,13719823343200698,89986405527666712,590148303249975384
%N A321116 Number of permutations p of [n] such that in 0p the largest up-jump equals nine xx and no down-jump is larger than 2.
%H A321116 Alois P. Heinz, <a href="/A321116/b321116.txt">Table of n, a(n) for n = 9..1000</a>
%p A321116 b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
%p A321116       add(b(u-j, o+j-1, k), j=1..min(2, u))+
%p A321116       add(b(u+j-1, o-j, k), j=1..min(k, o)))
%p A321116     end:
%p A321116 a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(9):
%p A321116 seq(a(n), n=9..30);
%Y A321116 Column k=9 of A291680.
%K A321116 nonn
%O A321116 9,1
%A A321116 _Alois P. Heinz_, Oct 27 2018