OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
Wikipedia, Permutation
FORMULA
EXAMPLE
a(2) = 1: (1)(2).
a(3) = 1: (1)(2)(3).
a(4) = 10: (1)(2)(3)(4), (1)(2)(3,4), (1)(2,4)(3), (1)(2,3)(4), (1,4)(2)(3), (1,3)(2)(4), (1,2)(3)(4), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+b(n-i, min(i-1, n-i))/i))
end:
a:= n-> n!*(1-b(n$2)):
seq(a(n), n=0..23);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
b[n, i - 1] + b[n - i, Min[i - 1, n - i]]/i]];
a[n_] := n!*(1 - b[n, n]);
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 24 2022
STATUS
approved