A255006
a(n) is the numerator of polygamma(2n+1, 1) / Pi^(2n+2).
Original entry on oeis.org
1, 1, 8, 8, 128, 176896, 2048, 3703808, 1437433856, 11443306496, 40728264704, 123922856542208, 5519125250048, 56921405366730752, 231279728174802403328, 258681888643685023744, 325620148558310146048, 113023230705723814256110993408
Offset: 0
Polygamma values {Pi^2/6, Pi^4/15, 8*Pi^6/63, 8*Pi^8/15, 128*Pi^10/33, ...} give numerators {1, 1, 8, 8, 128, ...} and denominators {6, 15, 63, 15, 33, ...}.
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a[n_] := PolyGamma[2n+1, 1] / Pi^(2n+2) // Numerator; Table[a[n], {n, 0, 20}]
A255008
Array T(n,k) read by ascending antidiagonals, where T(n,k) is the numerator of polygamma(n, 1) - polygamma(n, k).
Original entry on oeis.org
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
Offset: 0
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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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
A255009
Array T(n,k) read by ascending antidiagonals, where T(n,k) is the denominator of polygamma(n, 1) - polygamma(n, k).
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 1, 1, 4, 6, 1, 1, 4, 36, 12, 1, 1, 8, 108, 144, 60, 1, 1, 4, 216, 864, 3600, 20, 1, 1, 8, 324, 3456, 108000, 3600, 140, 1, 1, 8, 1944, 10368, 2160000, 12000, 176400, 280, 1, 1, 16, 1944, 124416, 32400000, 2160000, 4116000
Offset: 0
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T[n_, k_] := (-1)^(n+1)*n!*HarmonicNumber[k-1, n+1] // Denominator; Table[T[n-k, k], {n, 0, 10}, {k, 1, n}] // Flatten
Showing 1-3 of 3 results.
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