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 A036778 #38 Aug 07 2024 01:08:00
%S A036778 1,3,65,3787,427905,79549811,22036379521,8513206310715,
%T A036778 4374455745966593,2885264091484122979,2376040584184726335681,
%U A036778 2389484304129542889498923,2881763610489447544905661825,4105338427962827177938910410707,6820519958449287654130653696838145
%N A036778 Number of labeled rooted trees on 2n+1 nodes each node having an even number of children.
%D A036778 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.82).
%H A036778 Michael De Vlieger, <a href="/A036778/b036778.txt">Table of n, a(n) for n = 0..210</a>
%H A036778 Yiyang Jia and Jacobus J. M. Verbaarschot, <a href="https://arxiv.org/abs/1806.03271">Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs</a>, arXiv:1806.03271 [hep-th], 2018.
%H A036778 Yiyang Jia and Jacobus J. M. Verbaarschot, <a href="https://doi.org/10.1007/JHEP11(2018)031">Large N expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs</a>, J. High Energ. Phys. (2018) 2018: 31.
%H A036778 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, esp. Eq. (16).
%H A036778 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A036778 G.f.: REVERT(x/cosh(x)) = Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)!. - _Paul D. Hanna_, Oct 15 2003
%F A036778 a(n) = (1/2^(2*n+1)) * Sum_{k=0..2*n+1} binomial(2*n+1, k)*(2*k-2*n-1)^(2*n).
%p A036778 [ seq((1/2^(2*n+1))*add( binomial(2*n+1,j)*(2*j-(2*n+1))^(2*n),j=0..(2*n+1)), n=1..30) ];
%t A036778 Table[1/2^(2n+1) Sum[Binomial[2n+1,k](2k-2n-1)^(2n),{k,0,2n+1}],{n,0,20}] (* _Harvey P. Dale_, Mar 06 2012 *)
%o A036778 (PARI) a(n)=local(X); if(n<0,0,X=x+O(x^(2*n+1));(2*n+1)!*polcoeff(serreverse(x/cosh(x)),2*n+1)) \\ _Paul D. Hanna_, Oct 15 2003
%K A036778 nonn,eigen
%O A036778 0,2
%A A036778 _N. J. A. Sloane_
%E A036778 Edited by _Christian G. Bower_, Jan 13 2004