A036506 Number of labeled 4-trees with n nodes.

0, 0, 0, 1, 1, 15, 455, 20230, 1166886, 82031250, 6768679170, 639276644655, 67876292150095, 7992910154350121, 1032869077119140625, 145221924661653841820, 22060305511905816000860, 3599313659344525384083060, 627583654087024080928783956

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=4.

Links

• T. D. Noe, Table of n, a(n) for n=1..100
• Index entries for sequences related to trees

Crossrefs

Column 5 of A135021.

Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A078793 (unlabeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).

Programs

Python

def A036506(n): return int(n*(n - 3)*(n - 2)*(n - 1)*(4*n - 15)**(n - 6)//24) # Chai Wah Wu, Feb 03 2022

Formula

a(n) = C(n,4)*(4*n-15)^(n-6).

Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).