OFFSET
1,6
COMMENTS
For the statistic "length of the longest cycle", see A211871.
LINKS
Steven Finch, Permute, Graph, Map, Derange, arXiv:2111.05720 [math.CO], 2021.
D. Panario and B. Richmond, Exact largest and smallest size of components, Algorithmica, 31 (2001), 413-432.
FORMULA
EXAMPLE
Triangle begins:
0;
0, 1;
0, 0, 2;
0, 3, 0, 6;
0, 20, 0, 0, 24;
0, 105, 40, 0, 0, 120;
0, 714, 420, 0, 0, 0, 720;
0, 5845, 2688, 1260, 0, 0, 0, 5040;
0, 52632, 22400, 18144, 0, 0, 0, 0, 40320;
...
MAPLE
b:= proc(n, m) option remember; `if`(n=0, x^m, add((j-1)!*
b(n-j, min(m, j))*binomial(n-1, j-1), j=2..n))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n$2)):
seq(T(n), n=1..12); # Alois P. Heinz, Sep 27 2021
MATHEMATICA
b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[(j - 1)!*
b[n - j, Min[m, j]]*Binomial[n - 1, j - 1], {j, 2, n}]];
T[n_] := If[n == 1, {0}, CoefficientList[b[n, n], x] // Rest];
Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Oct 03 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Steven Finch, Sep 27 2021
STATUS
approved