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A158020
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Triangle of coefficients in expansion of (-1-x)^floor(n/2)(1-x)^ceil(n/2).
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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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 .
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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). - DELEHAM Philippe, Dec 02 2011
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EXAMPLE
| Triangle begins :
1
1, -1
-1, 0, 1
-1, 1, 1, -1
1, 0, -2, 0, 1 ...
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MATHEMATICA
| Flatten[Table[CoefficientList[(-1 - x)^Floor[n/2] (1 - x)^Ceiling[n/2], x], {n, 0, 11}]] (* T. D. Noe, Dec 01 2011 *)
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CROSSREFS
| Cf. A051160.
Sequence in context: A126306 A029402 A035196 * A051160 A051159 A035697
Adjacent sequences: A158017 A158018 A158019 * A158021 A158022 A158023
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KEYWORD
| sign,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 11 2009
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EXTENSIONS
| Corrected by DELEHAM Philippe, Dec 02 2011
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