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 A130525 #11 Jan 27 2025 21:15:04
%S A130525 1,3,13,63,324,1733,9541,53725,308085,1793528,10574165,63018105,
%T A130525 379061652,2298508911,14035748542,86240951745,532812883413,
%U A130525 3307967729867,20627845299471,129141164822496,811394148828087,5114638998643903,32336393838083539,205000199138736499,1302892014385402691
%N A130525 Diagonal immediately above the main diagonal of square array A130523.
%F A130525 G.f.: A(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 A130525 (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(D*F+x*O(x^n),n,x)}
%o A130525 for(n=0,25,print1(a(n),", "))
%Y A130525 Cf. A130523; diagonals: A007857, A130524; related: A000108, A001764.
%K A130525 nonn
%O A130525 0,2
%A A130525 _Paul D. Hanna_, Jun 02 2007
%E A130525 Edited and corrected by _Paul D. Hanna_, Jan 27 2025