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Search: id:A115071
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| A115071 |
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Numerator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) +...+ (n-1)^n/2 + n^n/1. |
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+0
6
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| 1, 9, 94, 3625, 18631, 1120581, 34793764, 5692787001, 29669041771, 30708223774261, 134127439064434, 302304605103335861, 2387352152511746837, 109134149200789179825, 24217460586461892638584
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OFFSET
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1,2
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COMMENT
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a(p-1) is divisible by p^3 for prime p>3. a(p^2-1) is divisible by p^6 for prime p>3. a(p^3-1) is divisible by p^9 for prime p>3.
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FORMULA
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a(n) = numerator[ Sum[ i^n/(n+1-i), {i,1,n}].
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EXAMPLE
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a(1) = numerator[1/1] = 1
a(2) = numerator[1/2 + 4/1] = 9
a(3) = numerator[1/3 + 4/2 + 9/1] = 94
a(4) = numerator[1/4 + 4/3 + 9/2 + 16/1] = 3625
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MATHEMATICA
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Table[Numerator[Sum[i^n/(n+1-i), {i, 1, n}]], {n, 1, 20}]
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CROSSREFS
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Cf. A001008, A027612.
Sequence in context: A048359 A099297 A057782 this_sequence A000562 A098450 A065456
Adjacent sequences: A115068 A115069 A115070 this_sequence A115072 A115073 A115074
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 17 2006
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