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A167568
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A triangle related to the GF(z) formulas of the rows of the ED2 array A167560.
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3
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1, 0, 2, 2, -2, 6, 0, 16, -16, 24, 24, -48, 144, -120, 120, 0, 432, -864, 1392, -960, 720, 720, -2160, 8208, -12816, 14448, -8400, 5040, 0, 23040, -69120, 149760, -184320, 161280, -80640, 40320, 40320, -161280, 760320, -1716480, 2684160, -2695680
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OFFSET
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1,3
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COMMENTS
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The GF(z) formulas given below correspond to the first ten rows of the ED2 array A167560. The polynomials in their numerators lead to the triangle given above.
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LINKS
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EXAMPLE
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Row 1: GF(z) = 1/(1-z).
Row 2: GF(z) = 2/(1-z)^2.
Row 3: GF(z) = (2*z^2 - 2*z + 6)/(1-z)^3.
Row 4: GF(z) = (0*z^3 + 16*z^2 - 16*z + 24)/(1-z)^4.
Row 5: GF(z) = (24*z^4 - 48*z^3 + 144*z^2 - 120*z + 120)/(1-z)^5.
Row 6: GF(z) = (432*z^4 - 864*z^3 + 1392*z^2 - 960*z + 720)/(1-z)^6.
Row 7: GF(z) = (720*z^6 - 2160*z^5 + 8208*z^4 - 12816*z^3 + 14448*z^2 - 8400*z + 5040)/(1-z)^7.
Row 8: GF(z) = (0*z^7 + 23040*z^6 - 69120*z^5 + 149760*z^4 - 184320*z^3 + 161280*z^2 - 80640*z + 40320)/(1-z)^8.
Row 9: GF(z) = (40320*z^8 - 161280*z^7 + 760320*z^6 - 1716480*z^5 + 2684160*z^4 - 2695680*z^3 + 1935360*z^2 - 846720*z + 362880)/(1-z)^9.
Row 10: GF(z) = (0*z^9 + 2016000*z^8 - 8064000*z^7 + 22464000*z^6 - 39168000*z^5 + 48360960*z^4 - 40849920*z^3 + 24917760*z^2 - 9676800*z + 3628800)/(1-z)^10.
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CROSSREFS
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A005359 equals the first left hand column.
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KEYWORD
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AUTHOR
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STATUS
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approved
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