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A122184
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Numerator of Sum_{k=0..2n} (-1)^k/C(2n,k)^3.
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0
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1, 15, 1705, 47789, 1369377, 213162301, 43005554527, 14505995375, 23869750002797, 2384790127843063, 624724994927411, 24386251366041479501, 2042595777439018142725, 11191251831905709132993
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| p^k divides a((p^k+1)/2) for prime p>2 and integer k>0.
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LINKS
| Eric Weisstein's World of Mathematics, Binomial Sums.
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FORMULA
| a(n) = Numerator[ Sum[ (-1)^k / Binomial[2n,k]^3, {k,0,2n} ] ].
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MATHEMATICA
| Table[ Numerator[ Sum[ (-1)^k / Binomial[2n, k]^3, {k, 0, 2n} ] ], {n, 0, 25} ]
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CROSSREFS
| Cf. A046825 = Numerator of Sum_{k=0..n} 1/C(n, k). Cf. A100516 = Numerator of Sum_{k=0..n} 1/C(n, k)^2. Cf. A100518 = Numerator of Sum_{k=0..n} 1/C(n, k)^3. Cf. A100520 = Numerator of Sum_{k=0..2n} (-1)^k/C(2n, k)^2.
Sequence in context: A205423 A195891 A195521 * A069450 A205346 A070862
Adjacent sequences: A122181 A122182 A122183 * A122185 A122186 A122187
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), May 10 2007
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