OFFSET
1,2
COMMENTS
Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..449
Wikipedia, Permutation
FORMULA
Recursion: see Maple program.
EXAMPLE
a(3) = 25 because the sum of the entries in the last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 6+6+3+2+5+3 = 25.
MAPLE
a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,
((2*n^2+3*n-1)*a(n-1)-(n+2)*(n-1)*n*a(n-2))/(n+1))
end:
seq(a(n), n=1..25);
MATHEMATICA
Table[n! * (n-1 + 2*(n+1)*HarmonicNumber[n])/4, {n, 1, 25}] (* Vaclav Kotesovec, Apr 29 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 20 2017
STATUS
approved