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Search: id:A054765
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| A054765 |
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a(n+2) = (2n+3)*a(n+1) + (n+1)^2*a(n). |
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+0
4
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| 0, 1, 3, 19, 160, 1744, 23184, 364176, 6598656, 135484416, 3108695040, 78831037440, 2189265960960, 66083318415360, 2154235544616960, 75425161203302400, 2822882994841190400, 112463980097804697600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The denominators of the convergents of [1/3, 4/5, 9/7, 16/9, ...]. To produce Pi the above continued fraction is used. It is formed by n^2/(2*n+1) which starts at n=1. Most numerators of continued fractions are 1 & thus are left out of the brackets. In the case of pi they vary. Therefore here both numerators & denominators are given. The first 4 convergents are 1/3,5/19,44/160,476/1744. The value of this continued fraction is .273239... . 4*INV(1+.273239...) is pi. - Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008
Starting with offset 1 = row sums of triangle A155729. [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), Jan 25 2009]
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LINKS
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K. S. Brown, Integer Sequences Related To PI
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CROSSREFS
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A155729 [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), Jan 25 2009]
Sequence in context: A113013 A105784 A077046 this_sequence A057719 A136474 A105624
Adjacent sequences: A054762 A054763 A054764 this_sequence A054766 A054767 A054768
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 26 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 27 2000
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