cp's OEIS Frontend

A320982 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of eight.

%I A320982 #4 Oct 25 2018 19:29:22
%S A320982 0,1,9,2061,20736,1507293,17118482,849597609,10896848134,459634150710,
%T A320982 6622740258098,260269850813548,4183025733598532,160312786582715100,
%U A320982 2852747036627655519,109305622312149855474,2138487419350175956196,83104784124134380097202
%N A320982 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of eight.
%H A320982 Alois P. Heinz, <a href="/A320982/b320982.txt">Table of n, a(n) for n = 8..451</a>
%F A320982 a(n) = A262133(n) - A262132(n).
%p A320982 b:= proc(u, o, c) option remember; `if`(c<0 or c>8, 0, `if`(u+o=0,
%p A320982        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..8))(add(
%p A320982        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A320982     end:
%p A320982 a:= n-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 8):
%p A320982 seq(a(n), n=8..30);
%Y A320982 Column k=8 of A262125.
%Y A320982 Cf. A262132, A262133.
%K A320982 nonn
%O A320982 8,3
%A A320982 _Alois P. Heinz_, Oct 25 2018