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A320981 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of seven.

%I A320981 #4 Oct 25 2018 19:25:25
%S A320981 0,1,8,1031,9379,486299,5084162,196352061,2352460536,81070646577,
%T A320981 1103813259377,36592927821767,560827842703887,18549898652794829,
%U A320981 317078625531545481,10667284286197389079,201655098112826170280,6973904694490809821089,144705018721890264334923
%N A320981 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of seven.
%H A320981 Alois P. Heinz, <a href="/A320981/b320981.txt">Table of n, a(n) for n = 7..452</a>
%F A320981 a(n) = A262132(n) - A262131(n).
%p A320981 b:= proc(u, o, c) option remember; `if`(c<0 or c>7, 0, `if`(u+o=0,
%p A320981        x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..7))(add(
%p A320981        b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
%p A320981     end:
%p A320981 a:= n-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 7):
%p A320981 seq(a(n), n=7..30);
%Y A320981 Column k=7 of A262125.
%Y A320981 Cf. A262131, A262132.
%K A320981 nonn
%O A320981 7,3
%A A320981 _Alois P. Heinz_, Oct 25 2018