A262164 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 2.

1, 1, 2, 4, 16, 54, 324, 1532, 12256, 74512, 745120, 5536752, 66441024, 583466480, 8168530720, 82769713504, 1324315416064, 15208157533440, 273746835601920, 3513491887566848, 70269837751336960, 996837786288583168, 21930431298348829696, 340730692136161864704

Offset: 0

Author

Alois P. Heinz, Sep 13 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..464

Crossrefs

Column k=2 of A262163.

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-> (p-> add(coeff(p, x, i), i=0..min(n, 2)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,2).