|
|
A285616
|
|
Triangle read by rows: T(n,k) is the number of hypergraphs on n labeled vertices with exactly k connected components, n>=1, 1<=k<=n.
|
|
0
|
|
|
2, 4, 4, 96, 24, 8, 31840, 816, 96, 16, 2147156736, 322240, 4320, 320, 32, 9223372011084915712, 25767883392, 1957440, 18240, 960, 64, 170141183460469231602560095199828453376, 129127208335656968192, 180389362944, 9251200, 67200, 2688, 128
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: A(x)^y where A(x) = Sum_{n>=0} 2^(2^n-1)x^n/n!.
|
|
EXAMPLE
|
Triangle begins:
2,
4, 4,
96, 24, 8,
31840, 816, 96, 16,
2147156736, 322240, 4320, 320, 32,
9223372011084915712, 25767883392, 1957440, 18240, 960, 64,
...
|
|
MATHEMATICA
|
nn = 6; A[z_] := Sum[2^(2^n - 1) z^n/n!, {n, 0, nn}];
Map[Select[#, # > 0 &] &, Drop[Range[0, nn]! CoefficientList[
Series[(A[z]^u), {z, 0, nn}], {z, u}], 1]] // Grid
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|