A321059 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=3.

2, 8, 64, 852, 17008, 467696, 16860608, 769534688, 43316046592, 2945846638464, 238048843712512, 22542120635302912, 2472277850712350720, 310880199760083564032, 44429722692959679590400, 7161345941202962487965696, 1292988538929694918729072640

Offset: 3

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn

Examples

			a(3) = 2: (312,312), (321,321).
a(4) = 8: (3124,3124), (3142,3142), (3142,3241), (3214,3214), (3241,3142), (3241,3241), (3412,3412), (3421,3421).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..110

Crossrefs

Column k=3 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))(3):
seq(a(n), n=3..20);