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%I #3 Mar 30 2012 18:37:04
%S 1,4,18,87,442,2332,12677,70605,401172,2317683,13578615,80502845,
%T 482140580,2912954090,17733363776,108674957854,669843377831,
%U 4148242390236,25757224787638,159544222448006,974349264795556
%N Diagonal immediately below the main diagonal of square array A130523.
%F G.f.: A(x) = C(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(C*D*F+x*O(x^n),n,x)}
%Y Cf. A130523; diagonals: A007857, A130525; related: A000108, A001764.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 02 2007
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