|
%I
%S 1,3,5,12,20,45,77,168,294,630,1122,2376,4290,9009,16445,34320,63206,
%T 131274,243542,503880,940576,1939938,3640210,7488432,14115100,
%U 28973100,54826020,112326480,213286590,436268025,830905245,1697168160,3241119750
%N Sum of root degrees of all symmetric ordered trees with n edges.
%F G.f.: z*C(z^2)^2*(1+2*z*C(z^2))/(1-z*C(z^2)), where C(z)=(1-sqrt(1-4*z))/(2*z) is the g.f. of the Catalan numbers (A000108).
%F a(n) = sum(k=1..n, k * A143359(n,k) ).
%F D-finite with recurrence 2*(n+3)*a(n) +(-n-5)*a(n-1) +(-11*n-3)*a(n-2) +2*(2*n+1)*a(n-3) +12*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jul 24 2022
%p C := z -> (1/2-(1/2)*sqrt(1-4*z))/z: G := z*C(z^2)^2*(1+2*z*C(z^2))/(1-z*C(z^2)): Gser := series(G, z=0, 40): seq(coeff(Gser, z, n), n=1..34);
%Y Cf. A000108, A129869 and A143359.
%K nonn
%O 1,2
%A _Emeric Deutsch_, Aug 15 2008
|
