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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. 1

%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^(n-2), hence the number of coefficients in row n > 1 is given by 2^(n-2) + 1 = A094373(n-1).

%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^(n-2)) divided by the polynomial p(n) are equal, i. e.

%C m + m/(m-1) = m * m/(m-1) = m^2/(m-1);

%C 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 The triangle T(n,k), k = 0..2^(n-1), 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^(n-2)); # n > 1

%p b(1):=m;

%p p:=proc(n) option remember; p(n-1)*a(n-1); 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

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Last modified June 19 05:16 EDT 2019. Contains 324217 sequences. (Running on oeis4.)