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A164942
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Triangle, read by rows, T(n,k) = (-1)^k*binomial(n, k)*3^(n-k).
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4
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1, 3, -1, 9, -6, 1, 27, -27, 9, -1, 81, -108, 54, -12, 1, 243, -405, 270, -90, 15, -1, 729, -1458, 1215, -540, 135, -18, 1, 2187, -5103, 5103, -2835, 945, -189, 21, -1, 6561, -17496, 20412, -13608, 5670, -1512, 252, -24, 1, 19683, -59049, 78732, -61236, 30618, -10206, 2268, -324, 27, -1
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OFFSET
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0,2
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COMMENTS
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Triangle, read by rows, given by [3,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 02 2009
Essentially the same as the inverse of A027465, but with opposite signs in every other row. - M. F. Hasler, Feb 17 2020
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LINKS
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FORMULA
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T(n,k) = (-1)^n*(Inverse of A027465).
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EXAMPLE
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Begins as triangle:
1;
3, -1;
9, -6, 1;
27, -27, 9, -1;
81, -108, 54, -12, 1;
243, -405, 270, -90, 15, -1;
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MAPLE
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seq(seq( (-1)^k*binomial(n, k)*3^(n-k), k=0..n), n=0..10); # G. C. Greubel, Feb 17 2020
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MATHEMATICA
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With[{m = 9}, CoefficientList[CoefficientList[Series[1/(1-3*x+x*y), {x, 0, m}, {y, 0, m}], x], y]] // Flatten (* Georg Fischer, Feb 17 2020 *)
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PROG
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(Magma) [(-1)^k*Binomial(n, k)*3^(n-k): k in [0..n], n in [0..10]]; // G. C. Greubel, Feb 17 2020
(Sage) [[(-1)^k*binomial(n, k)*3^(n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Feb 17 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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