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A119389
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Numerator of (1^2/n + 2^2/(n-1) + ... + k^2/(n-k+1) + ... + (n-1)^2/2 + n^2/1).
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0
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1, 9, 34, 265, 186, 1141, 2868, 31401, 18635, 477301, 91192, 8051069, 4508441, 3336145, 22048024, 410111791, 223063947, 3057889621, 823596665, 706952715, 125961187, 6173866701, 9838037952, 521135614075, 275363139571
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| p divides a(p-1) for prime p>2. p divides a(2p-1) for all prime p. p divides a(3p-1) for all prime p. p divides a(4p-1) for all prime p except p=3. p divides a(5p-1) for prime p>3. p divides a(6p-1) for all prime except p=5. . p^2 divides a(p^2-1) for prime p>2. p^2 divides a(2p^2-1) for all prime p. p^2 divides a(3p^2-1) for all prime p. . p^3 divides a(p^3-1) for prime p>2. . p^k divides a(p^k-1) for prime p>2 and integer k>1. p^k divides a(m*p^k-1) for all prime p and integer m,k>1.
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FORMULA
| a(n) = Numerator[Sum[k^2/(n-k+1),{k,1,n}]]. a(n) = Numerator[HarmonicNumber[n]*(n+1)^2 - 3*n(n+1)/2]. a(n) = Numerator[A001008[n]/A002805[n]*(n+1)^2 - 3*A000217[n]].
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MATHEMATICA
| Numerator[Table[Sum[k^2/(n-k+1), {k, 1, n}], {n, 1, 50}]]
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CROSSREFS
| Cf. A027612, A001008, A002805, A000217.
Sequence in context: A050478 A204426 A154393 * A197273 A067960 A119757
Adjacent sequences: A119386 A119387 A119388 * A119390 A119391 A119392
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 26 2006
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