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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.

%I A079628 #19 Aug 11 2015 13:43:49
%S A079628 1,1,-1,1,-3,2,1,-5,8,-4,1,-7,18,-20,8,1,-9,32,-56,48,-16,1,-11,50,
%T A079628 -120,160,-112,32,1,-13,72,-220,400,-432,256,-64,1,-15,98,-364,840,
%U A079628 -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
%N 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.
%C A079628 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
%F A079628 P(n, x)= (-1)^n*(x-1)*(2*x-1)^(n-1).
%F A079628 G.f.: (1+x*y)/(1+2*x*y-x). - _R. J. Mathar_, Aug 11 2015
%e A079628 det(M(4,x))=1-7x+18x^2-20x^3+8x^4.
%e A079628 1;
%e A079628 1,-1;
%e A079628 1,-3,2;
%e A079628 1,-5,8,-4;
%e A079628 1,-7,18,-20,8;
%e A079628 1,-9,32,-56,48,-16;
%e A079628 1,-11,50,-120,160,-112,32;
%e A079628 1,-13,72,-220,400,-432,256,-64;
%e A079628 1,-15,98,-364,840,-1232,1120,-576,128;
%e A079628 1,-17,128,-560,1568,-2912,3584,-2816,1280,-256,
%p A079628 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
%Y A079628 Cf. A081277.
%Y A079628 Cf. A167580 and A167591. - _Johannes W. Meijer_, Nov 23 2009
%K A079628 sign,tabl
%O A079628 0,5
%A A079628 _Benoit Cloitre_, Jan 30 2003
%E A079628 Sign added to formula. - _R. J. Mathar_, Nov 04 2011