This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A036506 #25 Mar 02 2024 13:10:38 %S A036506 0,0,0,1,1,15,455,20230,1166886,82031250,6768679170,639276644655, %T A036506 67876292150095,7992910154350121,1032869077119140625, %U A036506 145221924661653841820,22060305511905816000860,3599313659344525384083060,627583654087024080928783956 %N A036506 Number of labeled 4-trees with n nodes. %D A036506 F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 30, Problem 1.13(b) with k=4. %H A036506 T. D. Noe, <a href="/A036506/b036506.txt">Table of n, a(n) for n=1..100</a> %H A036506 <a href="/index/Tra#trees">Index entries for sequences related to trees</a> %F A036506 a(n) = C(n,4)*(4*n-15)^(n-6). %F A036506 Number of labeled k-trees on n nodes is binomial(n, k) * (k(n-k)+1)^(n-k-2). %o A036506 (Python) %o A036506 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 A036506 Column 5 of A135021. %Y A036506 Cf. A000272 (labeled trees), A036361 (labeled 2-trees), A036362 (labeled 3-trees), A078793 (unlabeled 4-trees), A000055 (unlabeled trees), A054581 (unlabeled 2-trees). %K A036506 nonn %O A036506 1,6 %A A036506 _N. J. A. Sloane_