%I #3 Mar 30 2012 18:37:04
%S 1,3,13,63,324,1733,9541,53725,308085,1793528,10574165,63018105,
%T 379061652,2298508872,14035737150,86239762294,532743452260,
%U 3305228985864,20546951820588,127237301998014,774257153670067
%N Diagonal immediately above the main diagonal of square array A130523.
%F G.f.: A(x) = D(x)*F(x), where D(x) = 1/[1 - xC(x)F(x) - xF(x)^2)] is the g.f. of the main diagonal (A007857), C(x) = 1 + xC(x)^2 is the g.f. of Catalan numbers (A000108) and F(x) = 1 + xF(x)^3 is the g.f. of ternary numbers (A001764).
%o (PARI) {a(n)=local(C,F,D); C=Ser(vector(n+1,r,binomial(2*r-2,r-1)/r)); F=Ser(vector(n+1,r,binomial(3*r-3,r-1)/(2*r-1))); D=1/(1-x*C*F-x*F^2);polcoeff(D*F+x*O(x^n),n,x)}
%Y Cf. A130523; diagonals: A007857, A130524; related: A000108, A001764.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 02 2007