[go: up one dir, main page]

login
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
OFFSET
1,5
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=3.
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
Column 4 of A135021.
Cf. A000272 (labeled trees), A036361 (labeled 2-trees), this sequence (labeled 3-trees), A036506 (labeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).
Sequence in context: A320671 A237025 A156275 * A051262 A367201 A362723
KEYWORD
nonn,easy
STATUS
approved