|
|
A334957
|
|
Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k self loops, n>=0, 0<=k<=n.
|
|
0
|
|
|
1, 1, 1, 4, 8, 4, 64, 192, 192, 64, 4096, 16384, 24576, 16384, 4096, 1048576, 5242880, 10485760, 10485760, 5242880, 1048576, 1073741824, 6442450944, 16106127360, 21474836480, 16106127360, 6442450944, 1073741824, 4398046511104, 30786325577728, 92358976733184, 153931627888640, 153931627888640, 92358976733184, 30786325577728, 4398046511104
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: g(x + y*x) where g(x) is the e.g.f. for A053763.
|
|
EXAMPLE
|
1,
1, 1,
4, 8, 4,
64, 192, 192, 64,
4096, 16384, 24576, 16384, 4096
|
|
MATHEMATICA
|
nn = 5; g[x_] := Sum[2^(n^2 - n) x^n/n!, {n, 0, nn}]; Map[Select[#, # > 0 &] &, Range[0, nn]! CoefficientList[Series[g[ x + y x], {x, 0, nn}], {x, y}]] // Grid
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|