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 A130524 #11 Jan 27 2025 21:14:56
%S A130524 1,4,18,87,442,2332,12677,70605,401172,2317683,13578615,80502845,
%T A130524 482140580,2912954129,17733375207,108676158775,669914021414,
%U A130524 4151053001800,25841001981211,161534820531068,1013566626969398,6381398103680604,40301852983776764,255249505209864803,1620819715569894894
%N A130524 Diagonal immediately below the main diagonal of square array A130523.
%F A130524 G.f.: A(x) = C(x)*D(x)*F(x), where D(x) = 1/(1 - x*C(x)*F(x) - x*F(x)^2) is the g.f. of the main diagonal (A007857), C(x) = 1 + x*C(x)^2 is the g.f. of Catalan numbers (A000108) and F(x) = 1 + x*F(x)^3 is the g.f. of ternary numbers (A001764).
%o A130524 (PARI) {a(n) = my(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); polcoef(C*D*F+x*O(x^n),n,x)}
%o A130524 for(n=0,25,print1(a(n),", "))
%Y A130524 Cf. A130523; diagonals: A007857, A130525; related: A000108, A001764.
%K A130524 nonn
%O A130524 0,2
%A A130524 _Paul D. Hanna_, Jun 02 2007
%E A130524 Edited and corrected by _Paul D. Hanna_, Jan 27 2025