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A321112 Number of permutations p of [n] such that in 0p the largest up-jump equals five and no down-jump is larger than 2.

%I A321112 #5 Oct 27 2018 16:17:48
%S A321112 10,58,340,2014,11888,69274,401648,2329526,13514794,78445016,
%T A321112 455726404,2650463368,15433424116,89977250572,525210971550,
%U A321112 3069436719818,17959557595206,105203403819650,616942677047888,3621795968081798,21283870741193560,125201162038738596
%N A321112 Number of permutations p of [n] such that in 0p the largest up-jump equals five and no down-jump is larger than 2.
%H A321112 Alois P. Heinz, <a href="/A321112/b321112.txt">Table of n, a(n) for n = 5..1000</a>
%p A321112 b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
%p A321112       add(b(u-j, o+j-1, k), j=1..min(2, u))+
%p A321112       add(b(u+j-1, o-j, k), j=1..min(k, o)))
%p A321112     end:
%p A321112 a:= n-> (k-> b(0, n, k)-b(0, n, k-1))(5):
%p A321112 seq(a(n), n=5..30);
%Y A321112 Column k=5 of A291680.
%K A321112 nonn
%O A321112 5,1
%A A321112 _Alois P. Heinz_, Oct 27 2018