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Search: id:A130036
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| A130036 |
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Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(3)/2. |
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4
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| 1, 16, 1024, 16384, 4194304, 67108864, 4294967296, 68719476736, 70368744177664, 1125899906842624, 72057594037927936, 1152921504606846976, 295147905179352825856, 4722366482869645213696, 302231454903657293676544
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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See the references and the W. Lang link under A130035.
Also denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and 1/2. For the numerators and the formula see A130037. Proof of the coincidence: The prefactor of each term of the sum (first formula in A130037) is binomial(2*n,n)^2, a natural number, and 3 will never divide the even denominators.
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FORMULA
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a(n) = denom(sum((((2*j)!/(j!^2))^2)*(1/2^(6*j)),j=0..n)), n>=0.
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CROSSREFS
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Sequence in context: A024301 A070307 A067490 this_sequence A013735 A029701 A053903
Adjacent sequences: A130033 A130034 A130035 this_sequence A130037 A130038 A130039
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jun 01 2007
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