A320979 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of five.

0, 1, 6, 254, 1835, 47673, 416221, 9565156, 99383961, 2250472801, 27333591309, 635688426842, 8878319017022, 215812184750821, 3416973303551969, 87455366666951644, 1550782738938548075, 41903722165381482287, 823596208419940694670, 23503436481574417378942

Offset: 5

Author

Alois P. Heinz, Oct 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..453

Crossrefs

Column k=5 of A262125.

Cf. A262129, A262130.

Programs

Maple

b:= proc(u, o, c) option remember; `if`(c<0 or c>5, 0, `if`(u+o=0,
       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..5))(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, 5):
seq(a(n), n=5..30);

Formula

a(n) = A262130(n) - A262129(n).