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A316394 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of seven.

%I A316394 #5 Jul 01 2018 16:37:14
%S A316394 1,7,522,4260,163871,1572713,49601660,554432537,16431601190,
%T A316394 211104220038,6214132488281,90601727479330,2718687446733807,
%U A316394 44477388811619142,1378374571651666083,25055072909382001747,807272266530396465622,16165637154045080226474
%N A316394 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of seven.
%H A316394 Alois P. Heinz, <a href="/A316394/b316394.txt">Table of n, a(n) for n = 7..451</a>
%F A316394 a(n) = A262169(n) - A262168(n).
%p A316394 b:= proc(u, o, c, k) option remember;
%p A316394       `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
%p A316394        add(b(u-j, o-1+j, c+1, k), j=1..u)+
%p A316394        add(b(u+j-1, o-j, c-1, k), j=1..o)))
%p A316394     end:
%p A316394 a:= n-> b(n, 0$2, 7)-b(n, 0$2, 6):
%p A316394 seq(a(n), n=7..24);
%Y A316394 Column k=7 of A258829.
%Y A316394 Cf. A262168, A262169.
%K A316394 nonn
%O A316394 7,2
%A A316394 _Alois P. Heinz_, Jul 01 2018