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A321066 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=10.

%I A321066 #6 Oct 27 2018 15:57:31
%S A321066 1035227008,48904686848,2945846638464,218405906177792,
%T A321066 19438574276705792,2038137238577944576,248048061418810109952,
%U A321066 34621419911316556017664,5486719044572824902107136,978934483626207520876986368,195206678980725195413273903104
%N A321066 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=10.
%H A321066 Alois P. Heinz, <a href="/A321066/b321066.txt">Table of n, a(n) for n = 10..110</a>
%p A321066 b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
%p A321066       add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
%p A321066       add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
%p A321066     end:
%p A321066 a:= n-> (k-> b(k-1, n-k, n-k))(10):
%p A321066 seq(a(n), n=10..20);
%Y A321066 Column k=10 of A262372.
%K A321066 nonn
%O A321066 10,1
%A A321066 _Alois P. Heinz_, Oct 26 2018