|
|
A215858
|
|
Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles.
|
|
3
|
|
|
1, 36, 1110, 31680, 904299, 26603148, 821278744, 26864874465, 935625630797, 34750489933016, 1375999952017938, 57998361908305494, 2596646585329104847, 123180358220543885268, 6175880603945440333627, 326438846760992348696038, 18147404450341079958539275
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
8,2
|
|
LINKS
|
|
|
EXAMPLE
|
a(9) = 36: each graph has one 2-node tree and 7 1-node trees and C(9,2) = 36.
|
|
MAPLE
|
T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
`if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
`if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
end:
a:= n-> T(n, 8):
seq(a(n), n=8..25);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|