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 A225200 #12 Jun 28 2023 08:25:40 %S A225200 1,-1,1,1,-1,1,1,-2,2,-1,1,1,-4,8,-10,9,-6,3,-1,1,1,-8,32,-84,162, %T A225200 -244,298,-302,258,-188,118,-64,30,-12,4,-1,1,1,-16,128,-680,2692, %U A225200 -8456,21924,-48204,91656,-152952,226580,-300664,359992,-391232,387820,-352074,293685,-225696,160120,-105024,63750,-35832,18654,-8994,4014,-1656,630,-220,70,-20,5,-1,1 %N A225200 Triangle (read by rows) of coefficients of the polynomials (in ascending order) of the denominators of the generalized sequence of fractions f(n) defined recursively by f(1) = m/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225200 The degree of the polynomial in row n > 1 is 2^(n-2), hence the number of coefficients in row n > 1 is given by 2^(n-2) + 1 = A094373(n-1). %C A225200 For n > 2 a new row always begins and ends with 1. %C A225200 The sum and product of the generalized sequence of fractions given by m^(2^(n-2)) divided by the polynomial p(n) are equal, i.e., %C A225200 m + m/(m-1) = m * m/(m-1) = m^2/(m-1); %C A225200 m + m/(m-1) + m^2/(m^2-m+1) = m * m/(m-1) * m^2/(m^2-m+1) = m^4/(m^3-2*m^2+2*m-1). %e A225200 The triangle T(n,k), k = 0..2^(n-1), begins %e A225200 1; %e A225200 -1, 1; %e A225200 1, -1, 1; %e A225200 1, -2, 2, -1, 1; %e A225200 1, -4, 8, -10, 9, -6, 3, -1, 1; %p A225200 b:=n->m^(2^(n-2)); # n > 1 %p A225200 b(1):=m; %p A225200 p:=proc(n) option remember; p(n-1)*a(n-1); end; %p A225200 p(1):=1; %p A225200 a:=proc(n) option remember; b(n)-p(n); end; %p A225200 a(1):=1; %p A225200 seq(op(PolynomialTools[CoefficientList](a(i),m,termorder=forward)),i=1..7); %Y A225200 Cf. A100441, A225156, A225157, A225158, A225159, A225160, A225161, A225162, A225201. %K A225200 sign,tabf %O A225200 1,8 %A A225200 _Martin Renner_, May 01 2013