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

5,3

Links

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

Formula

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

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);

Crossrefs

Column k=5 of A262125.

Cf. A262129, A262130.

Sequence in context: A332563 A041853 A168476 * A279869 A271501 A113900

Adjacent sequences: A320976 A320977 A320978 * A320980 A320981 A320982

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved