%I
%S 1,3,8,21,56,150,400,1065,2840,7578,20208,53874,143664,383148,1021728,
%T 2724465,7265240,19374450,51665200,137772246,367392656,979719348,
%U 2612584928,6966873546,18578329456,49542281220,132112749920
%N A Chebyshev transform of 3^n.
%F G.f.: c(x^2)/(13xc(x^2)), c(x) g.f. of Catalan numbers A000108; a(n)=sum{k=0..n, (k+1)C(n, n/2k/2)(1)^(n/2k/2)(1+(1)^(n+k))3^k/(n+k+2)}.
%F Conjecture: 3*(n+1)*a(n) 8*(n+1)*a(n1) +12*(n2)*a(n2) +32*(2n)*a(n3)=0.  _R. J. Mathar_, Sep 27 2012
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 05 2003
