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A255008
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Array T(n,k) read by ascending antidiagonals, where T(n,k) is the numerator of polygamma(n, 1) - polygamma(n, k).
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3
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0, 0, -1, 0, 1, -3, 0, -2, 5, -11, 0, 6, -9, 49, -25, 0, -24, 51, -251, 205, -137, 0, 120, -99, 1393, -2035, 5269, -49, 0, -720, 975, -8051, 22369, -256103, 5369, -363, 0, 5040, -5805, 237245, -257875, 14001361, -28567, 266681, -761, 0, -40320
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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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Fraction giving T(n,k) = polygamma(n, 1) - polygamma(n, k) = (-1)^(n+1)*n! * sum_{j=1..k-1} 1/j^(n+1) = (-1)^(n+1)*n!*H(k-1, n+1), where H(n,r) gives the n-th harmonic number of order r.
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EXAMPLE
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Array of fractions begin:
0, -1, -3/2, -11/6, -25/12, -137/60, ...
0, 1, 5/4, 49/36, 205/144, 5269/3600, ...
0, -2, -9/4, -251/108, -2035/864, -256103/108000, ...
0, 6, 51/8, 1393/216, 22369/3456, 14001361/2160000, ...
0, -24, -99/4, -8051/324, -257875/10368, -806108207/32400000, ...
0, 120, 975/8, 237245/1944, 15187325/124416, 47463376609/388800000, ...
...
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MATHEMATICA
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T[n_, k_] := (-1)^(n+1)*n!*HarmonicNumber[k-1, n+1] // Numerator; Table[T[n-k, k], {n, 0, 10}, {k, 1, n}] // Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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