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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
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OFFSET
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3,2
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LINKS
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FORMULA
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a(n) = numerator( Sum_{k=1..prime(n)} ( 1/binomial( k + prime(n) - 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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PROG
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(PARI) for(n=3, 10, print1(numerator(sum(k=1, prime(n), 1/(binomial(k+ prime(n)-1, prime(n)))))/prime(n)^4, ", ")) \\ G. C. Greubel, Nov 25 2017
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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