A103717
Denominators of sum_{k=1..n} 1/k^10 = Zeta(10,n).
Original entry on oeis.org
1, 1024, 60466176, 61917364224, 604661760000000000, 604661760000000000, 170801981216778240000000000, 174901228765980917760000000000, 10327742657402407212810240000000000, 413109706296096288512409600000000
Offset: 1
A322265
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = numerator of Sum_{j=1..n} 1/j^k.
Original entry on oeis.org
1, 1, 2, 1, 3, 3, 1, 5, 11, 4, 1, 9, 49, 25, 5, 1, 17, 251, 205, 137, 6, 1, 33, 1393, 2035, 5269, 49, 7, 1, 65, 8051, 22369, 256103, 5369, 363, 8, 1, 129, 47449, 257875, 14001361, 28567, 266681, 761, 9, 1, 257, 282251, 3037465, 806108207, 14011361, 9822481, 1077749, 7129, 10
Offset: 1
Square array begins:
1, 1, 1, 1, 1, ...
2, 3/2, 5/4, 9/8, 17/16, ...
3, 11/6, 49/36, 251/216, 1393/1296, ...
4, 25/12, 205/144, 2035/1728, 22369/20736, ...
5, 137/60, 5269/3600, 256103/216000, 14001361/12960000, ...
Columns k=0..10 give
A000027,
A001008,
A007406,
A007408,
A007410,
A099828,
A103345,
A103347,
A103349,
A103351,
A103716.
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Table[Function[k, Numerator[Sum[1/j^k, {j, 1, n}]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
Table[Function[k, Numerator[HarmonicNumber[n, k]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
Table[Function[k, Numerator[SeriesCoefficient[PolyLog[k, x]/(1 - x), {x, 0, n}]]][i - n], {i, 0, 10}, {n, 1, i}] // Flatten
Showing 1-2 of 2 results.
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