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Search: id:A118583
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| A118583 |
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Numerator of sum of first p reciprocals of p-simplex numbers divided by p^4, where p = Prime[n] for n>2. |
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1
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| 1, 5, 53, 789, 237493, 2576561, 338350897, 616410400171, 2603853251291, 5745400286707685, 3081677433937346539, 41741941495866750557, 7829195555633964779233, 21066131970056662377432067
(list; graph; listen)
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OFFSET
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3,2
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics, Composition.
Eric Weisstein, Link to a section of The World of Mathematics, Tetrahedral Number.
Eric Weisstein, Link to a section of The World of Mathematics, Triangular Number.
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FORMULA
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a(n) = Numerator[ Sum[ 1/Binomial[ k+Prime[n]-1, Prime[n] ], {k,1,Prime[n]} ] ] / Prime[n]^4 for n>2.
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EXAMPLE
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Prime[3] = 5.
a(3) = 1 because A118431(5)/5^4 = 1, where A118431(5) = Numerator[ 1/C(4+1,5) + 1/C(4+2,5) + 1/C(4+3,5) + 1/C(4+4,5) +1/C(4+5,5) ] = Numerator[ 1/1 + 1/6 + 1/21 + 1/56 + 1/126 ] = 625.
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MATHEMATICA
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Table[ Numerator[ Sum[1 /Binomial[ n+Prime[k]-1, Prime[k] ], {n, 1, Prime[k]} ] ] / Prime[k]^4, {k, 3, 25} ]
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CROSSREFS
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Cf. A022998 = Numerator of sum of reciprocals of first n triangular numbers Cf. A118391 = Numerator of sum of reciprocals of first n tetrahedral numbers A000292. Cf. A118431 = Numerator of sum of reciprocals of first n 5-simplex numbers A000389.
Sequence in context: A123788 A036910 A036916 this_sequence A090360 A123130 A094089
Adjacent sequences: A118580 A118581 A118582 this_sequence A118584 A118585 A118586
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 09 2007
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