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A316392 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of five.

%I A316392 #5 Jul 01 2018 14:04:35
%S A316392 1,5,129,819,16066,127538,2423226,23367449,459383574,5246611332,
%T A316392 109138956326,1446115120862,32069014233249,484780196858918,
%U A316392 11478459399841878,195255855453716821,4931560739013573590,93326559046408832001,2509294817575539112099
%N A316392 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of five.
%H A316392 Alois P. Heinz, <a href="/A316392/b316392.txt">Table of n, a(n) for n = 5..453</a>
%F A316392 a(n) = A262167(n) - A262166(n).
%p A316392 b:= proc(u, o, c, k) option remember;
%p A316392       `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
%p A316392        add(b(u-j, o-1+j, c+1, k), j=1..u)+
%p A316392        add(b(u+j-1, o-j, c-1, k), j=1..o)))
%p A316392     end:
%p A316392 a:= n-> b(n, 0$2, 5)-b(n, 0$2, 4):
%p A316392 seq(a(n), n=5..23);
%Y A316392 Column k=5 of A258829.
%Y A316392 Cf. A262166, A262167.
%K A316392 nonn
%O A316392 5,2
%A A316392 _Alois P. Heinz_, Jul 01 2018