|
%I #25 Mar 02 2024 13:10:38
%S 0,0,0,1,1,15,455,20230,1166886,82031250,6768679170,639276644655,
%T 67876292150095,7992910154350121,1032869077119140625,
%U 145221924661653841820,22060305511905816000860,3599313659344525384083060,627583654087024080928783956
%N Number of labeled 4-trees with n nodes.
%D F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=4.
%H T. D. Noe, <a href="/A036506/b036506.txt">Table of n, a(n) for n=1..100</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = C(n,4)*(4*n-15)^(n-6).
%F Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2).
%o (Python)
%o def A036506(n): return int(n*(n - 3)*(n - 2)*(n - 1)*(4*n - 15)**(n - 6)//24) # _Chai Wah Wu_, Feb 03 2022
%Y Column 5 of A135021.
%Y Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A078793 (unlabeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees).
%K nonn
%O 1,6
%A _N. J. A. Sloane_
|
