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.

1, 0, 0, 0, 0, 0, 28, 239, 2789, 24970, 247089, 2289028, 23926282, 244031780, 2795283827, 32671509063, 426329260855, 5714045982473, 86176948036417, 1327311505233240, 22831768389870460, 401597165962560396, 7782893107559342148, 153285768850390602735, 3316598607281771351415

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..140

Formula

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

Maple

b:= proc(o, u, t, k) option remember; `if`(u+o=0, `if`(k=0,
       max(0, t-1)!, 0), `if`(t>0, b(u+o, 0$2, k)*(t-1)!, 0)+
       add(`if`(k+1<u+j, 0, b(o-j, u+j-1, t+1, k-(u+j-1))),
         j=`if`(t=0, 1, 1..o)))
    end:
a:= n-> b(n, 0$2, n):
seq(a(n), n=0..30);

Crossrefs

Main diagonal of A381529.

Sequence in context: A024015 A223347 A242436 * A119544 A112797 A085438

Adjacent sequences: A381542 A381543 A381544 * A381546 A381547 A381548

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2025

Status

approved