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A220962
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Faulhaber’s triangle: triangle of numerators of coefficients of power-sum polynomials.
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5
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0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, -1, 0, 1, 1, 1, 0, 0, -1, 0, 5, 1, 1, 0, 1, 0, -1, 0, 1, 1, 1, 0, 0, 1, 0, -7, 0, 7, 1, 1, 0, -1, 0, 2, 0, -7, 0, 2, 1, 1, 0, 0, -3, 0, 1, 0, -7, 0, 3, 1, 1, 0, 5, 0, -1, 0, 1, 0, -1, 0, 5, 1, 1
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OFFSET
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0,25
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COMMENTS
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LINKS
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EXAMPLE
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Rows start:
0,1;
0,1,1;
0,1,1,1;
0,0,1,1,1;
0,-1,0,1,1,1;
0,0,-1,0,5,1,1;
0,1,0,-1,0,1,1,1;
0,0,1,0,-7,0,7,1,1;
0,-1,0,2,0,-7,0,2,1,1;
...
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MATHEMATICA
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f[n_, x_] := f[n, x]=((x + 1)^(n + 1) - 1)/(n + 1) - Sum[Binomial[n + 1, k]*f[k, x], {k , 0, n - 1}]/(n + 1); f[0, x_] := x; row[n_] := CoefficientList[f[n, x], x] // Numerator; Table[row[n], {n, 0, 10}] // Flatten
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CROSSREFS
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KEYWORD
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sign,tabf,frac
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AUTHOR
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STATUS
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approved
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