|
|
A036362
|
|
Number of labeled 3-trees with n nodes.
|
|
9
|
|
|
0, 0, 1, 1, 10, 200, 5915, 229376, 10946964, 618435840, 40283203125, 2968444272640, 243926836708126, 22100985366992896, 2187905889450121295, 234881024000000000000, 27172548942138551952680, 3369317755618569294053376, 445726953911853022186520169
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
REFERENCES
|
F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=3.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = binomial(n, 3)*(3*n-8)^(n-5).
Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
|
|
MAPLE
|
[ seq(binomial(n, 3)*(3*n-8)^(n-5), n=1..20) ];
|
|
MATHEMATICA
|
Table[Binomial[n, 3](3n-8)^(n-5), {n, 20}] (* Harvey P. Dale, Dec 31 2023 *)
|
|
PROG
|
(Python)
def A036362(n): return int(n*(n - 2)*(n - 1)*(3*n - 8)**(n - 5)//6) # Chai Wah Wu, Feb 03 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|