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Search: id:A133818
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| A133818 |
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a(n) = (8*n+3)*(8*n+5)*(8*n+7)*(8*n+9). |
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+0
2
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| 945, 36465, 229425, 801009, 2070705, 4456305, 8473905, 14737905, 23961009, 36954225, 54626865, 77986545, 108139185, 146289009, 193738545, 251888625, 322238385, 406385265, 506025009, 622951665, 759057585, 916333425, 1096868145
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Also 1/3-1/5-1/7+1/9+1/11-1/13-1/15+1/17+1/19--++... = Pi*sqrt(2)/4-1 - Miklos Kristof (kristmikl(AT)freemail.hu), Sep 15 2008
Also sum(2*(-1)^n/((4*n+3)*(4*n+5)), n=0..infinity) = Pi*sqrt(2)/4-1 - Miklos Kristof (kristmikl(AT)freemail.hu), Sep 15 2008
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FORMULA
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G.f.: G(x) = 3*(315+10580*x+18850*x^2+3028*x^3-5*x^4)/(1-x)^5 E.g.f: E(x) = (945+35520*x+78720*x^2+36864*x^3+4096*x^4)*exp(x)
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MAPLE
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seq((8*n+3)*(8*n+5)*(8*n+7)*(8*n+9), n=0..30);
sum(32*(4*n+3)/((8*n+3)*(8*n+5)*(8*n+7)*(8*n+9)), n=0..infinity) = Pi*sqrt(2)/4-1. Maple: evalf(Pi*sqrt(2)/4-1, 30); gives 0.11072073453959156175397024752... - Miklos Kristof (kristmikl(AT)freemail.hu), Sep 15 2008
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CROSSREFS
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Adjacent sequences: A133815 A133816 A133817 this_sequence A133819 A133820 A133821
Sequence in context: A127667 A109729 A127666 this_sequence A112491 A133353 A119240
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KEYWORD
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easy,nonn,new
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Jan 06 2008, Sep 15 2008
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EXTENSIONS
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More terms from Miklos Kristof (kristmikl(AT)freemail.hu), Sep 15 2008
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