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

%I A262379 #4 Sep 20 2015 13:17:19
%S A262379 1,1,8,852,438496,678914816,2475764410944,18237517555977472,
%T A262379 244043425473888612352,5486719044572824902107136,
%U A262379 195206678980725195413273903104,10481263341014180286866656598294528,817228517264548077840269973629276061696
%N A262379 Number of ordered pairs (p,q) of permutations of [2n] with equal up-down signatures and p(1)=q(1)=n.
%H A262379 Alois P. Heinz, <a href="/A262379/b262379.txt">Table of n, a(n) for n = 0..55</a>
%F A262379 a(n) = A262372(2n,n).
%e A262379 a(2) = 8: (2134,2134), (2143,2143), (2314,2314), (2314,2413), (2341,2341), (2413,2314), (2413,2413), (2431,2431).
%p A262379 b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
%p A262379       add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
%p A262379       add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
%p A262379     end:
%p A262379 a:= n-> `if`(n=0, 1, b(n-1, n, n)):
%p A262379 seq(a(n), n=0..15);
%Y A262379 Cf. A262372.
%K A262379 nonn
%O A262379 0,3
%A A262379 _Alois P. Heinz_, Sep 20 2015