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

2,3

Links

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

Formula

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

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);

Crossrefs

Column k=2 of A262125.

Cf. A000111, A262126.

Sequence in context: A374488 A216725 A334038 * A164938 A342112 A050545

Adjacent sequences: A320973 A320974 A320975 * A320977 A320978 A320979

Keyword

nonn

Author

Alois P. Heinz, Oct 25 2018

Status

approved