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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
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, -244, 298, -302, 258, -188, 118, -64, 30, -12, 4, -1, 1, 1, -16, 128, -680, 2692, -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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

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).

For n > 2 a new row begins and ends always with 1.

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.

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

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).

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

The triangle T(n,k), k = 0..2^(n-1), begins

1;

-1, 1;

1, -1, 1;

1, -2, 2, -1, 1;

1, -4, 8, -10, 9, -6, 3, -1, 1;

MAPLE

b:=n->m^(2^(n-2)); # n > 1

b(1):=m;

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

p(1):=1;

a:=proc(n) option remember; b(n)-p(n); end;

a(1):=1;

seq(op(PolynomialTools[CoefficientList](a(i), m, termorder=forward)), i=1..7);

CROSSREFS

Cf. A100441, A225156 to A225162, A225201.

Sequence in context: A104320 A242618 A180264 * A128706 A253586 A318191

Adjacent sequences:  A225197 A225198 A225199 * A225201 A225202 A225203

KEYWORD

sign,tabf

AUTHOR

Martin Renner, May 01 2013

STATUS

approved

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)