A321060 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=4.

10, 68, 852, 16328, 438496, 15608288, 707767328, 39729927744, 2700561836672, 218405906177792, 20715182759975936, 2276573425946788864, 286926691657095745024, 41104621803491951127552, 6641412815937114696669184, 1201977736831477123144658944

Offset: 4

Author

Alois P. Heinz, Oct 26 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..110

Crossrefs

Column k=4 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))(4):
seq(a(n), n=4..20);