A381545 Number of permutations of [n] having exactly n pairs of integers i

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

Author

Alois P. Heinz, Feb 26 2025

Keywords

• nonn

Links

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

Crossrefs

Main diagonal of A381529.

Programs

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 b(n, 0$2, n):
seq(a(n), n=0..30);

Formula

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