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 A143360 #22 Apr 09 2024 06:31:26
%S A143360 1,3,5,12,20,45,77,168,294,630,1122,2376,4290,9009,16445,34320,63206,
%T A143360 131274,243542,503880,940576,1939938,3640210,7488432,14115100,
%U A143360 28973100,54826020,112326480,213286590,436268025,830905245,1697168160,3241119750,6611884290
%N A143360 Sum of root degrees of all symmetric ordered trees with n edges.
%F A143360 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 A143360 a(n) = Sum_{k=1..n} k * A143359(n,k).
%F A143360 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 A143360 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);
%t A143360 Module[{nmax = 33, G, C}, G = z*C[z^2]^2*(1 + 2*z*C[z^2])/(1 - z*C[z^2]); C[z_] = (1/2-(1/2)*Sqrt[1-4*z])/z; CoefficientList[G/z + O[z]^nmax, z]] (* _Jean-François Alcover_, Apr 09 2024 *)
%Y A143360 Cf. A000108, A129869 and A143359.
%K A143360 nonn
%O A143360 1,2
%A A143360 _Emeric Deutsch_, Aug 15 2008