A158020 - OEIS

A158020

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

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, 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, 0, -10, 0, 10, 0, -5, 0, 1, -1, 1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1

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OFFSET

0,13

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..77.

FORMULA

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

G.f.: (1+(1-y)*x)/(1+(1-y^2)*x^2). - Philippe Deléham, Dec 02 2011

EXAMPLE

Triangle begins:

1, -1;

-1, 0, 1;

-1, 1, 1, -1;

1, 0, -2, 0, 1; ...

MATHEMATICA