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Search: id:A038534
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| A038534 |
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Numerators of coefficients of EllipticK/Pi. |
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+0
6
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| 1, 1, 9, 25, 1225, 3969, 53361, 184041, 41409225, 147744025, 2133423721, 7775536041, 457028729521, 1690195005625, 25145962430625, 93990019574025, 90324408810638025, 340357374376418025, 5147380044581630625, 19520119892056100625
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also, numerators in expansion of hypergeometric series 2F1(1/2,1/2; 1; x).
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 91, Eq. 2.1.
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FORMULA
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a(n) = 2^(-2 w[n])Binomial[2n, n]^2 with w[n]=A000120 = number of 1's in binary expansion of n
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MATHEMATICA
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Numerator@ CoefficientList[ Series[ EllipticK@x, {x, 0, 19}]/Pi, x] (* Robert G. Wilson v (rgwv@rgwv.com), Jul 19 2007 *)
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CROSSREFS
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Equals A001790(n)^2.
Cf. A038533, A038535.
Sequence in context: A014760 A013397 A048056 this_sequence A117755 A144701 A022421
Adjacent sequences: A038531 A038532 A038533 this_sequence A038535 A038536 A038537
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KEYWORD
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frac,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), revised Jan 03 2001
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