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A051160
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Coefficients in expansion of (1-x)^floor(n/2)(1+x)^ceil(n/2).
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9
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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, 1, 0, -6, 0, 15, 0, -20
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OFFSET
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0,13
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COMMENTS
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Triangle T(n,k), 0<=k<=n, read by rows given by [1,0,-1,0,0,0,0,0,...]DELTA[1,-2,1,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . [From Philippe DELEHAM, Sep 22 2008]
The production matrix for this array has bivariate e.g.f. equal to exp(-t*x)*(1-t). [From Paul Barry, Nov 22 2008]
The elements of the matrix inverse are apparently T^(-1)(n,k) = (-1)^(n+k)*T(n,k). - R. J. Mathar, Apr 08 2013
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LINKS
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Table of n, a(n) for n=0..84.
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FORMULA
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T(n, k) = -T(n-2, k-2) + T(n-2, k). T(0, 0) = T(1, 0) = T(1, 1) = 1.
T(n,k)=T(n-1,k)+(-1)^(n-1)T(n-1,k-1) T(0,0)=1. - Jose Ramon Real, Nov 10 2007
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EXAMPLE
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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;
...
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MAPLE
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A051160 := proc(n, k)
(1-x)^floor(n/2)*(1+x)^ceil(n/2) ;
coeftayl(%, x=0, k) ;
end proc: # R. J. Mathar, Apr 08 2013
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PROG
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(PARI) {T(n, k) = polcoeff( (1 - x)^(n\2) * (1 + x)^ceil(n/2), k)}
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CROSSREFS
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Cf. A007318, A051159(n, k)=(-1)^[ k/2 ]*T(n, k).
Sequence in context: A029402 A035196 A158020 * A051159 A035697 A135549
Adjacent sequences: A051157 A051158 A051159 * A051161 A051162 A051163
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Michael Somos, Oct 14 1999
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STATUS
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approved
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