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Search: id:A051160
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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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+0
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
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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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 (kolotoko(AT)wanadoo.fr), Sep 22 2008]
The production matrix for this array has bivariate e.g.f. equal to exp(-t*x)*(1-t). [From Paul Barry (pbarry(AT)wit.ie), Nov 22 2008]
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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 (joseramonreal(AT)yahoo.es), 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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PROGRAM
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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 ]*A051160(n, k).
Sequence in context: A029402 A035196 A158020 this_sequence A051159 A035697 A135549
Adjacent sequences: A051157 A051158 A051159 this_sequence 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
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