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A316395 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of eight.

%I A316395 #5 Jul 01 2018 17:39:34
%S A316395 1,8,1040,9468,507355,5313447,214378961,2571977379,92953037066,
%T A316395 1265907917962,44038999833044,674142774632948,23379215615715958,
%U A316395 398561935596289153,14037530250073013445,264291741199540446059,9551899031473405653870,197148463934806397523934
%N A316395 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of eight.
%H A316395 Alois P. Heinz, <a href="/A316395/b316395.txt">Table of n, a(n) for n = 8..451</a>
%F A316395 a(n) = A262170(n) - A262169(n).
%p A316395 b:= proc(u, o, c, k) option remember;
%p A316395       `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
%p A316395        add(b(u-j, o-1+j, c+1, k), j=1..u)+
%p A316395        add(b(u+j-1, o-j, c-1, k), j=1..o)))
%p A316395     end:
%p A316395 a:= n-> b(n, 0$2, 8)-b(n, 0$2, 7):
%p A316395 seq(a(n), n=8..25);
%Y A316395 Column k=8 of A258829.
%Y A316395 Cf. A262169, A262170.
%K A316395 nonn
%O A316395 8,2
%A A316395 _Alois P. Heinz_, Jul 01 2018