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Search: id:A095159
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| A095159 |
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Numerator of b(n) given by b(1) = 1, b(2) = 2; for n >= 3, b(n) = (-1)^n (2n-1) ((n-2)!!)^2/((n-1)!!)^2, where n!! is the double factorial A006882. |
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+0
2
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| 1, 2, -5, 28, -81, 704, -325, 768, -20825, 311296, -83349, 1507328, -1334025, 3145728, -5337189, 130023424, -1366504425, 7516192768, -5466528925, 12884901888, -87470372561, 2954937499648, -349899121845, 12919261626368, -22394407746529, 52776558133248, -89580335298125
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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b(n) is such that the continued fraction [b(1); b(2), b(3),..., b(n)] is equal to sum{k=1 to n} 1/k = H(n) = the n_th harmonic number, for all positive integers n.
a(2n)/A095175(2n) -> pi as n -> inf.; a(2n+1)/A095175(2n+1) -> -4/pi as n -> inf. - Leroy Quet Aug 03 2004
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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1, 2, -5/4, 28/9, -81/64, 704/225, -325/256, 768/245, -20825/16384, 311296/99225, ...
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CROSSREFS
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Cf. A006882, A095175.
Sequence in context: A127357 A025170 A151775 this_sequence A047132 A072371 A019043
Adjacent sequences: A095156 A095157 A095158 this_sequence A095160 A095161 A095162
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), based on a suggestion of Leroy Quet, Jul 03 2004
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