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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved