|
|
A216520
|
|
Triangular array read by rows, T(n,k) = number of partial functions on {1,2,...,n} with exactly k cycles.
|
|
1
|
|
|
1, 1, 1, 3, 5, 1, 16, 35, 12, 1, 125, 328, 149, 22, 1, 1296, 3894, 2125, 425, 35, 1, 16807, 56221, 35044, 8555, 970, 51, 1, 262144, 958152, 661878, 186809, 26180, 1918, 70, 1, 4782969, 18849384, 14145858, 4467092, 731059, 66836, 3430, 92, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Here we consider the directed graphs of partial functions on {1,2,...,n} where the undefined points are mapped to a special value (forming a forest).
Row sums = (n+1)^n.
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: exp(T(x))/(1 - T(x))^y where T(x) is the e.g.f. for A000169.
|
|
EXAMPLE
|
1,
1, 1,
3, 5, 1,
16, 35, 12, 1,
125, 328, 149, 22, 1,
1296, 3894, 2125, 425, 35, 1,
16807, 56221, 35044, 8555, 970, 51, 1
|
|
MATHEMATICA
|
nn=6; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[Exp[t]/(1-t)^y, {x, 0, nn}], {x, y}] //Grid
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|