A320976 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of two.

0, 1, 3, 24, 101, 862, 4743, 47216, 322039, 3744368, 30517747, 409498400, 3884904379, 59360223088, 642766195887, 11046815693568, 134468538125519, 2571506053105408, 34764547687430955, 732881798335913984, 10895866774781276947, 251184536044504689152

Offset: 2

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..464

Crossrefs

Column k=2 of A262125.

Cf. A000111, A262126.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>2, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..2))(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, 2):
seq(a(n), n=2..30);

Formula

a(n) = A262126(n) - A000111(n).