A262379 Number of ordered pairs (p,q) of permutations of [2n] with equal up-down signatures and p(1)=q(1)=n.

1, 1, 8, 852, 438496, 678914816, 2475764410944, 18237517555977472, 244043425473888612352, 5486719044572824902107136, 195206678980725195413273903104, 10481263341014180286866656598294528, 817228517264548077840269973629276061696

Offset: 0

Author

Alois P. Heinz, Sep 20 2015

Keywords

• nonn

Examples

			a(2) = 8: (2134,2134), (2143,2143), (2314,2314), (2314,2413), (2341,2341), (2413,2314), (2413,2413), (2431,2431).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..55

Crossrefs

Cf. 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-> `if`(n=0, 1, b(n-1, n, n)):
seq(a(n), n=0..15);

Formula

a(n) = A262372(2n,n).