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A079628 Array of coefficients of P(n,x) = det (M(n,x)) where M(n,x) is the n X n matrix m(i,j)=x if i>j m(i,j)=1-x if i<=j. 4
1, 1, -1, 1, -3, 2, 1, -5, 8, -4, 1, -7, 18, -20, 8, 1, -9, 32, -56, 48, -16, 1, -11, 50, -120, 160, -112, 32, 1, -13, 72, -220, 400, -432, 256, -64, 1, -15, 98, -364, 840, -1232, 1120, -576, 128, 1, -17, 128, -560, 1568, -2912, 3584, -2816, 1280, -256, 1, -19, 162, -816, 2688, -6048, 9408, -9984, 6912, -2816, 512, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Formatted as a triangular array, this is [1, 0, 0, 0, 0, 0, 0, ...] DELTA [ -1, -1, 0, 0, 0, 0, 0, 0, ...] (see construction in A084938). - Philippe Deléham, Aug 09 2005

LINKS

Table of n, a(n) for n=0..66.

FORMULA

P(n, x)= (-1)^n*(x-1)*(2*x-1)^(n-1).

G.f.: (1+x*y)/(1+2*x*y-x). - R. J. Mathar, Aug 11 2015

EXAMPLE

det(M(4,x))=1-7x+18x^2-20x^3+8x^4.

1;

1,-1;

1,-3,2;

1,-5,8,-4;

1,-7,18,-20,8;

1,-9,32,-56,48,-16;

1,-11,50,-120,160,-112,32;

1,-13,72,-220,400,-432,256,-64;

1,-15,98,-364,840,-1232,1120,-576,128;

1,-17,128,-560,1568,-2912,3584,-2816,1280,-256,

MAPLE

A079628 := proc(n, k) local x; expand((-1)^n* (x-1)*(2*x-1)^(n-1)) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Nov 04 2011

CROSSREFS

Cf. A081277.

Cf. A167580 and A167591. - Johannes W. Meijer, Nov 23 2009

Sequence in context: A232206 A209559 A081277 * A140287 A077951 A077976

Adjacent sequences:  A079625 A079626 A079627 * A079629 A079630 A079631

KEYWORD

sign,tabl

AUTHOR

Benoit Cloitre, Jan 30 2003

EXTENSIONS

Sign added to formula. - R. J. Mathar, Nov 04 2011

STATUS

approved

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Last modified January 21 16:54 EST 2020. Contains 331114 sequences. (Running on oeis4.)