A262479 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=2.

1, 2, 8, 68, 952, 19312, 533544, 19209584, 873274112, 48904686848, 3307732742656, 265835173240320, 25041294346380800, 2732759857218994176, 342041866136488863232, 48672372916773453011968, 7813786873387535522529280, 1405550552561695118460387328

Offset: 2

Author

Alois P. Heinz, Sep 30 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..150

Crossrefs

Column k=2 of A262372.

Programs

Maple

b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
      add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
      add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
    end:
a:= n-> (k-> b(k-1, n-k, n-k))(2):
seq(a(n), n=2..20);