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A074799
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a(n) = numerator( (4*n+1)*(Product_{i=1..n} (2*i-1)/Product_{i=1..n} 2*i)^5 ).
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4
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1, 5, 2187, 40625, 892871875, 20841167403, 16443713753775, 421390226721321, 364130196991193221875, 9816949116755633084375, 8619392462988365485907909, 239904481399203205153660455
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OFFSET
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0,2
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REFERENCES
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Bruce C. Berndt and Robert Rankin, "Ramanujan : letters and commentary", AMS-LMS, History of mathematics vol. 9, p. 57
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..335
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FORMULA
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a(n) = numerator of (b(n)), where b(n) = (4*n+1)*(Product_{i=1..n} (2*i - 1)/Product_{i=1..n} 2*i)^5 and b(0) = 1.
1 + Sum_{k>=1} (-1)^k*b(k) = 2/gamma(3/4)^4 = 0.88694116857811540541...
a(n) = numerator( (4*n+1)*( binomial(2*n, n)/4^n )^5 ). - G. C. Greubel, Jul 09 2021
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MATHEMATICA
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Table[Numerator[(4*n+1)*(Binomial[2*n, n]/4^n)^5], {n, 0, 30}] (* G. C. Greubel, Jul 09 2021 *)
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PROG
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(PARI) a(n)=numerator((4*n+1)*(prod(i=1, n, 2*i-1)/prod(i=1, n, 2*i))^5)
(Magma) [Numerator((4*n+1)*((n+1)*Catalan(n)/4^n)^5): n in [0..30]]; // G. C. Greubel, Jul 09 2021
(Sage) [numerator((4*n+1)*(binomial(2*n, n)/4^n)^5) for n in (0..30)] # G. C. Greubel, Jul 09 2021
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CROSSREFS
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Cf. A074800 (denominators).
Sequence in context: A247106 A266170 A114428 * A172942 A067944 A260843
Adjacent sequences: A074796 A074797 A074798 * A074800 A074801 A074802
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Benoit Cloitre, Sep 08 2002
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STATUS
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approved
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