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 A377461 #28 Aug 09 2025 04:00:12
%S A377461 1,1,2,9,54,540,6480,113400,2268000,61236000,1837080000,70727580000,
%T A377461 2970558360000,154469034720000,8650265944320000,583892951241600000,
%U A377461 42040292489395200000,3573424861598592000000,321608237543873280000000,33608060823334757760000000
%N A377461 Number of ranked labeled trees compatible with the 2-leaf perfect phylogeny of sample size n that possesses the largest number of compatible ranked labeled trees.
%C A377461 The 2-leaf perfect phylogeny of sample size n that possesses the largest number of compatible ranked labeled trees is (floor(n/2), ceiling(n/2)); a(n) is the number of ranked labeled trees for this perfect phylogeny.
%H A377461 J. A. Palacios, A. Bhaskar, F. Disanto and N. A. Rosenberg, <a href="https://doi.org/10.1007/s00285-022-01748-w">Enumeration of binary trees compatible with a perfect phylogeny</a>, J. Math. Biol. 84 (2022), 54.
%F A377461 a(n) = ((n-2)! / ((floor(n/2)-1)! (n-1-floor(n/2))!)) * (floor(n/2))! (floor(n/2)-1)! (ceiling(n/2))! (ceiling(n/2)-1)! / (2^(floor(n/2)-1) 2^(ceiling(n/2)-1)).
%F A377461 a(n) = A001405(n-2)*A006472(floor(n/2))*A006472(ceiling(n/2)).
%F A377461 a(2n) = A306266(n).
%t A377461 a[n_] := ((n - 2)!/((Floor[n/2] - 1)! (n - 1 - Floor[n/2])!)) Product[Binomial[i, 2], {i, 2, Floor[n/2]}] Product[Binomial[i, 2], {i, 2, Ceiling[n/2]}]
%t A377461 a[n_] := ((n - 2)!/((Floor[n/2] - 1)! (n - 1 - Floor[n/2])!)) Floor[n/2]! (Floor[n/2] - 1)! Ceiling[n/2]! (Ceiling[n/2] - 1)! /(2^(Floor[n/2] - 1) 2^(Ceiling[n/2] - 1))
%Y A377461 Cf. A001405, A006472, A306266.
%K A377461 nonn
%O A377461 2,3
%A A377461 _Noah A Rosenberg_, Jan 03 2025