%I
%S 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 244,298,302,258,188,118,64,30,12,4,1,1,1,16,128,680,2692,
%U 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 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 The degree of the polynomial in row n > 1 is 2^(n2), hence the number of coefficients in row n > 1 is given by 2^(n2) + 1 = A094373(n1).
%C For n > 2 a new row begins and ends always with 1.
%C The sum and product of the generalized sequence of fractions given by m^(2^(n2)) divided by the polynomial p(n) are equal, i. e.
%C m + m/(m1) = m * m/(m1) = m^2/(m1);
%C m + m/(m1) + m^2/(m^2m+1) = m * m/(m1) * m^2/(m^2m+1) = m^4/(m^32*m^2+2*m1).
%e The triangle T(n,k), k = 0..2^(n1), begins
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 2, 1, 1;
%e 1, 4, 8, 10, 9, 6, 3, 1, 1;
%p b:=n>m^(2^(n2)); # n > 1
%p b(1):=m;
%p p:=proc(n) option remember; p(n1)*a(n1); end;
%p p(1):=1;
%p a:=proc(n) option remember; b(n)p(n); end;
%p a(1):=1;
%p seq(op(PolynomialTools[CoefficientList](a(i),m,termorder=forward)),i=1..7);
%Y Cf. A100441, A225156 to A225162, A225201.
%K sign,tabf
%O 1,8
%A _Martin Renner_, May 01 2013
