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A291448
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Triangle read by rows, denominators of coefficients (in rising powers) of rational polynomials P(n,x) such that Integral_{x=0..1} P'(n,x) = BernoulliMedian(n).
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7
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1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 11, 1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 11, 1, 13, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 11, 1, 13, 1, 1, 1, 1, 1, 3, 1, 5, 1, 1, 1, 1, 1, 11, 1, 13, 1, 1
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = Denominator([x^k] Integral(Sum_{j=0..n}(-1)^(n-j)*Stirling2(n,j)*j!*x^j)^m) for m = 2, n >= 0 and k = 0..m*n+1.
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EXAMPLE
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Triangle starts:
[1, 1]
[1, 1, 1, 3]
[1, 1, 1, 3, 1, 5]
[1, 1, 1, 3, 1, 5, 1, 7]
[1, 1, 1, 3, 1, 5, 1, 7, 1, 1]
[1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 11]
[1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 11, 1, 13]
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MAPLE
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MATHEMATICA
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T[n_] := Integrate[Sum[(-1)^(n-j+1) StirlingS2[n, j] j! x^j, {j, 0, n}]^2, x];
Trow[n_] := CoefficientList[T[n], x] // Denominator;
Table[Trow[r], {r, 0, 7}] // Flatten
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CROSSREFS
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KEYWORD
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nonn,tabf,frac
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AUTHOR
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STATUS
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approved
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