A262169 Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 7.

1, 1, 2, 5, 20, 87, 522, 3271, 26167, 214946, 2148500, 21869553, 262040897, 3184440794, 44442180413, 627992981034, 9996086297542, 161044694650665, 2877551846402242, 52059368659632095, 1031291013069584902, 20699996793232418643, 450130761784158558067

Offset: 0

Author

Alois P. Heinz, Sep 13 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..451

Crossrefs

Column k=7 of A262163.

Programs

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-> (p-> add(coeff(p, x, i), i=0..min(n, 7)))(b(0, n, 0)):
seq(a(n), n=0..25);

Formula

a(n) = A262163(n,7).