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A262170 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 8.

%I A262170 #4 Sep 14 2015 16:57:01
%S A262170 1,1,2,5,20,87,522,3271,26168,214954,2149540,21879021,262548252,
%T A262170 3189754241,44656559374,630564958413,10089039334608,162310602568627,
%U A262170 2921590846235286,52733511434265043,1054670228685300860,21098558728828707796,464168292034231571512
%N A262170 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 8.
%H A262170 Alois P. Heinz, <a href="/A262170/b262170.txt">Table of n, a(n) for n = 0..400</a>
%F A262170 a(n) = A262163(n,8).
%p A262170 b:= proc(u, o, c) option remember; `if`(c<0 or c>8, 0, `if`(u+o=0,
%p A262170        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..8))(add(
%p A262170        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A262170     end:
%p A262170 a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 8)))(b(0, n, 0)):
%p A262170 seq(a(n), n=0..25);
%Y A262170 Column k=8 of A262163.
%K A262170 nonn
%O A262170 0,3
%A A262170 _Alois P. Heinz_, Sep 13 2015