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A158020 Triangle of coefficients in expansion of (-1-x)^floor(n/2)(1-x)^ceiling(n/2). 3

%I

%S 1,1,-1,-1,0,1,-1,1,1,-1,1,0,-2,0,1,1,-1,-2,2,1,-1,-1,0,3,0,-3,0,1,-1,

%T 1,3,-3,-3,3,1,-1,1,0,-4,0,6,0,-4,0,1,1,-1,-4,4,6,-6,-4,4,1,-1,-1,0,5,

%U 0,-10,0,10,0,-5,0,1,-1,1,5,-5,-10,10,10,-10,-5,5,1,-1

%N Triangle of coefficients in expansion of (-1-x)^floor(n/2)(1-x)^ceiling(n/2).

%C Triangle T(n,k), 0 <= k <= n, read by rows given by [1,-2,1,0,0,0,0,0,0,...] DELTA [-1,0,1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

%F T(n,k) = T(n-2,k-2) - T(n-2,k), T(0,0)=T(1,0)=1, T(1,1)=-1.

%F G.f.: (1+(1-y)*x)/(1+(1-y^2)*x^2). - _Philippe Deléham_, Dec 02 2011

%e Triangle begins:

%e 1;

%e 1, -1;

%e -1, 0, 1;

%e -1, 1, 1, -1;

%e 1, 0, -2, 0, 1; ...

%t Flatten[Table[CoefficientList[(-1 - x)^Floor[n/2] (1 - x)^Ceiling[n/2], x], {n, 0, 11}]] (* _T. D. Noe_, Dec 01 2011 *)

%Y Cf. A051160.

%K sign,tabl

%O 0,13

%A _Philippe Deléham_, Mar 11 2009

%E Corrected by _Philippe Deléham_, Dec 02 2011

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Last modified May 22 22:13 EDT 2022. Contains 353959 sequences. (Running on oeis4.)