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 A036772 #41 Jul 08 2025 21:57:12
%S A036772 1,5,2520,9909900,150089940000,6217438242015000,574985352122181000000,
%T A036772 103753754577643425255000000,33189544956070738228953960000000,
%U A036772 17517292900368819935211385551000000000,14427024664929016470240101675459976000000000
%N A036772 Number of labeled rooted trees with a degree constraint: ((4*n)!/(24^n)) * binomial(4*n+1, n).
%H A036772 L. Takacs, <a href="http://www.appliedprobability.org/data/files/TMS%20articles/18_1_1.pdf ">Enumeration of rooted trees and forests</a>, Math. Scientist 18 (1993), 1-10; see Eq. (13) on p. 4 (with r = 4).
%H A036772 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A036772 From _Petros Hadjicostas_, Jun 08 2019: (Start)
%F A036772 Recurrence (with no interpolated zeros): -8 * (4*n + 1) * (4*n + 3)^2 * (2*n + 1)^2 * (4*n + 5) * a(n) + (81*n^2 + 162*n + 72) * a(n + 1) = 0 for n >= 0 with a(0) = 1.
%F A036772 E.g.f. (with interpolated zeros): Let G(x) = Sum_{n >= 0} a(n)*x^(4*n + 1)/(4*n + 1)!. Then the e.g.f. satisfies G(x) = x * (1 + G(x)^4/4!).
%F A036772 (End)
%t A036772 Table[(4n)!/24^n Binomial[4n+1,n],{n,0,10}] (* _Harvey P. Dale_, Aug 10 2011 *)
%Y A036772 Cf. A036770, A036771, A036773.
%K A036772 nonn
%O A036772 0,2
%A A036772 _N. J. A. Sloane_