cp's OEIS Frontend

A262168 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 6.

%I A262168 #4 Sep 14 2015 14:46:19
%S A262168 1,1,2,5,20,87,522,3270,26160,214424,2144240,21705682,260468184,
%T A262168 3134839134,43887747876,611561379844,9784982077504,154830562162384,
%U A262168 2786950118922912,49340681212898288,986813624257965760,19321622221580752560,425075688874776556320
%N A262168 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 6.
%H A262168 Alois P. Heinz, <a href="/A262168/b262168.txt">Table of n, a(n) for n = 0..452</a>
%F A262168 a(n) = A262163(n,6).
%p A262168 b:= proc(u, o, c) option remember; `if`(c<0 or c>6, 0, `if`(u+o=0,
%p A262168        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..6))(add(
%p A262168        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A262168     end:
%p A262168 a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 6)))(b(0, n, 0)):
%p A262168 seq(a(n), n=0..25);
%Y A262168 Column k=6 of A262163.
%K A262168 nonn
%O A262168 0,3
%A A262168 _Alois P. Heinz_, Sep 13 2015