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

%I A321060 #5 Oct 27 2018 14:29:42
%S A321060 10,68,852,16328,438496,15608288,707767328,39729927744,2700561836672,
%T A321060 218405906177792,20715182759975936,2276573425946788864,
%U A321060 286926691657095745024,41104621803491951127552,6641412815937114696669184,1201977736831477123144658944
%N A321060 Number of ordered pairs (p,q) of permutations of [n] with equal up-down signatures and p(1)=q(1)=4.
%H A321060 Alois P. Heinz, <a href="/A321060/b321060.txt">Table of n, a(n) for n = 4..110</a>
%p A321060 b:= proc(u, o, h) option remember; `if`(u+o=0, 1,
%p A321060       add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h), j=1..u)+
%p A321060       add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o))
%p A321060     end:
%p A321060 a:= n-> (k-> b(k-1, n-k, n-k))(4):
%p A321060 seq(a(n), n=4..20);
%Y A321060 Column k=4 of A262372.
%K A321060 nonn
%O A321060 4,1
%A A321060 _Alois P. Heinz_, Oct 26 2018