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A381545 Number of permutations of [n] having exactly n pairs of integers i in [n] such that their cycle minima have opposite sorting order.

%I A381545 #10 Feb 27 2025 17:05:11
%S A381545 1,0,0,0,0,0,28,239,2789,24970,247089,2289028,23926282,244031780,
%T A381545 2795283827,32671509063,426329260855,5714045982473,86176948036417,
%U A381545 1327311505233240,22831768389870460,401597165962560396,7782893107559342148,153285768850390602735,3316598607281771351415
%N A381545 Number of permutations of [n] having exactly n pairs of integers i<j in [n] such that their cycle minima have opposite sorting order.
%H A381545 Alois P. Heinz, <a href="/A381545/b381545.txt">Table of n, a(n) for n = 0..140</a>
%F A381545 a(n) = A381529(n,n).
%p A381545 b:= proc(o, u, t, k) option remember; `if`(u+o=0, `if`(k=0,
%p A381545        max(0, t-1)!, 0), `if`(t>0, b(u+o, 0$2, k)*(t-1)!, 0)+
%p A381545        add(`if`(k+1<u+j, 0, b(o-j, u+j-1, t+1, k-(u+j-1))),
%p A381545          j=`if`(t=0, 1, 1..o)))
%p A381545     end:
%p A381545 a:= n-> b(n, 0$2, n):
%p A381545 seq(a(n), n=0..30);
%Y A381545 Main diagonal of A381529.
%K A381545 nonn
%O A381545 0,7
%A A381545 _Alois P. Heinz_, Feb 26 2025