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A318147
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Coefficients of the Omega polynomials of order 3, triangle T(n,k) read by rows with 0<=k<=n.
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2
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1, 0, 1, 0, -9, 10, 0, 477, -756, 280, 0, -74601, 142362, -83160, 15400, 0, 25740261, -55429920, 40900860, -12612600, 1401400, 0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400, 190590400
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OFFSET
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0,5
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COMMENTS
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The name 'Omega polynomial' is not a standard name.
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LINKS
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FORMULA
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Omega(m, n, z) = (m*n)!*[z^(n*m)] H(m, z)^x where H(m, z) = hypergeom([], [seq(i/m, i=1..m-1)], (z/m)^m). We consider here the case m = 3 (for other cases see the cross-references).
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EXAMPLE
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[0] [1]
[1] [0, 1]
[2] [0, -9, 10]
[3] [0, 477, -756, 280]
[4] [0, -74601, 142362, -83160, 15400]
[5] [0, 25740261, -55429920, 40900860, -12612600, 1401400]
[6] [0, -16591655817, 38999319642, -33465991104, 13440707280, -2572970400,190590400]
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MAPLE
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# See A318146 for the missing functions.
FL([seq(CL(OmegaPolynomial(3, n)), n=0..8)]);
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MATHEMATICA
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(* OmegaPolynomials are defined in A318146 *)
Table[CoefficientList[OmegaPolynomial[3, n], x], {n, 0, 6}] // Flatten
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PROG
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(Sage)
# See A318146 for the function OmegaPolynomial.
[list(OmegaPolynomial(3, n)) for n in (0..6)]
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CROSSREFS
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All row sums are 1, alternating row sums (taken absolute) are A002115.
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KEYWORD
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AUTHOR
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STATUS
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approved
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