A381545 - OEIS

%I #10 Feb 27 2025 17:05:11

%S 1,0,0,0,0,0,28,239,2789,24970,247089,2289028,23926282,244031780,

%T 2795283827,32671509063,426329260855,5714045982473,86176948036417,

%U 1327311505233240,22831768389870460,401597165962560396,7782893107559342148,153285768850390602735,3316598607281771351415

%N 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 Alois P. Heinz, <a href="/A381545/b381545.txt">Table of n, a(n) for n = 0..140</a>

%F a(n) = A381529(n,n).

%p b:= proc(o, u, t, k) option remember; `if`(u+o=0, `if`(k=0,

%p        max(0, t-1)!, 0), `if`(t>0, b(u+o, 0$2, k)*(t-1)!, 0)+

%p        add(`if`(k+1<u+j, 0, b(o-j, u+j-1, t+1, k-(u+j-1))),

%p          j=`if`(t=0, 1, 1..o)))

%p     end:

%p a:= n-> b(n, 0$2, n):

%p seq(a(n), n=0..30);

%Y Main diagonal of A381529.

%K nonn

%O 0,7

%A _Alois P. Heinz_, Feb 26 2025