This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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