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.

0, 1, 8, 1031, 9379, 486299, 5084162, 196352061, 2352460536, 81070646577, 1103813259377, 36592927821767, 560827842703887, 18549898652794829, 317078625531545481, 10667284286197389079, 201655098112826170280, 6973904694490809821089, 144705018721890264334923

Offset: 7

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..452

Crossrefs

Column k=7 of A262125.

Cf. A262131, A262132.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>7, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..7))(add(
       b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
    end:
a:= n-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 7):
seq(a(n), n=7..30);

Formula

a(n) = A262132(n) - A262131(n).