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