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.

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

Offset: 0

Author

Benoit Cloitre, Jan 30 2003

Keywords

• sign
• tabl

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

Examples

			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,
		

Crossrefs

Cf. A081277.

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

Programs

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

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

Extensions

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