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 A286012 #12 Jun 17 2017 02:11:46 %S A286012 1,1,1,1,2,2,1,3,6,3,1,4,12,17,5,1,5,20,48,50,8,1,6,30,102,197,147,13, %T A286012 1,7,42,185,532,815,434,21,1,8,56,303,1165,2804,3391,1282,34 %N A286012 A Kedlaya-Wilf matrix for the Fibonacci sequence A000045. %C A286012 For any power series f(x) starting with the term x the first column of the Kedlaya-Wilf matrix are the coefficients of f(x), the second column are the coefficients of f(f(x)), the third column are the coefficients of f(f(f(x))) and so on. This gives a matrix with first row consisting of ones. The sequence given is the diagonal reading of this matrix from right up to left down. %H A286012 Kiran S. Kedlaya, <a href="https://doi.org/10.1006/jcta.1999.3029">Another Combinatorial Determinant</a>, Journal of Combinatorial Theory Series A 90(1), November 1998. %F A286012 As an n X n matrix a(i,j) = coefficient of x^i in f^(j)(x) for i,j=1..n where f^(j) is the j-fold composition of f with itself. %e A286012 f^(3)(x) = x + 3x^2 + 12x^4 + ... as in A283679, so a(4)=1, a(8)=3, a(13)=12. %p A286012 h:= x-> x/(1-x-x^2): %p A286012 h2:= n-> coeff(series(h(h(x))), x, n+1), x, n): %p A286012 h3:= n -> coeff(series(h(h2(x))),x,n+1), x, n): %p A286012 etc. %p A286012 h7:= n -> coeff(series(h(h6(x))),x,n+1), x, n): N7:=array(1..7,1..7,sparse): gg:=array([h1,h2,h3,h4,h5,h6,h7]):for k from 1 to 7 do: for j from 1 to 7 do: N7[k,j]:=coeff(series(gg[j],x,12),x^k): od:od: %Y A286012 Cf. A000045, A270863, A283679. %K A286012 nonn,tabl,more %O A286012 1,5 %A A286012 _Oboifeng Dira_, Apr 30 2017