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

7,3

Links

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

Formula

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

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);

Crossrefs

Column k=7 of A262125.

Cf. A262131, A262132.

Sequence in context: A122067 A076688 A004808 * A316395 A176372 A047943

Adjacent sequences: A320978 A320979 A320980 * A320982 A320983 A320984

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved