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

%I A262479 #23 Oct 26 2018 21:46:40
%S A262479 1,2,8,68,952,19312,533544,19209584,873274112,48904686848,
%T A262479 3307732742656,265835173240320,25041294346380800,2732759857218994176,
%U A262479 342041866136488863232,48672372916773453011968,7813786873387535522529280,1405550552561695118460387328
%N A262479 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=2.
%H A262479 Alois P. Heinz, <a href="/A262479/b262479.txt">Table of n, a(n) for n = 2..150</a>
%p A262479 b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
%p A262479       add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
%p A262479       add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
%p A262479     end:
%p A262479 a:= n-> (k-> b(k-1, n-k, n-k))(2):
%p A262479 seq(a(n), n=2..20);
%Y A262479 Column k=2 of A262372.
%K A262479 nonn
%O A262479 2,2
%A A262479 _Alois P. Heinz_, Sep 30 2015