%I A036778
%S A036778 1,3,65,3787,427905,79549811,22036379521,8513206310715,4374455745966593,
%T A036778 2885264091484122979,2376040584184726335681,2389484304129542889498923,
%U A036778 2881763610489447544905661825,4105338427962827177938910410707,6820519958449287654130653696838145
%N A036778 Number of labeled rooted trees on 2n+1 nodes each node having an even 
               number of children.
%D A036778 L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 
               (1993), 1-10, esp. Eq. (16).
%D A036778 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Cambridge, 1998, p. 185 (3.1.82)
%H A036778 <a href="Sindx_Ro.html#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 (pauldhanna(AT)juno.com), 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) ];
%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)) (from Paul Hanna)
%Y A036778 Sequence in context: A112000 A012804 A012837 this_sequence A065400 A091470 
               A028567
%Y A036778 Adjacent sequences: A036775 A036776 A036777 this_sequence A036779 A036780 
               A036781
%K A036778 nonn,eigen
%O A036778 0,2
%A A036778 N. J. A. Sloane (njas(AT)research.att.com).
%E A036778 Edited by Christian G. Bower (bowerc(AT)usa.net), Jan 13 2004