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Search: id:A087547
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| A087547 |
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a(n) = n!*2^(n+1) * (Integral_{x = 0..1} 1/(1+x^2)^(n+1) dx - pi*(2*n)!/(2^(n+1)*n!). |
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+0
2
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| 0, 1, 4, 22, 160, 1464, 16224, 211632, 3179520, 54092160, 1028113920, 21594021120, 496702402560, 12418039065600, 335293281792000, 9723592350259200, 301432670532403200, 9947299050359193600, 348155822449999872000, 12881771833023700992000, 502389223133024747520000
(list; graph; listen)
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OFFSET
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0,3
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EXAMPLE
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a(3) = 22.
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MAPLE
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f := proc(n) 4*n!*2^(n-1) * (int (1/(1+x^2)^(n+1), x=0..1)) - Pi*(2*n)!/(2^(n+1)*n!); end; (from njas)
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MATHEMATICA
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f[n_] := Simplify[n!*2^(n + 1)*(Integrate[ 1/(1 + x^2)^(n + 1), {x, 0, 1}]) - Pi(2n)!/(2^(n + 1)*n!)]; Table[ f[n], {n, 0, 20}] (from Robert G. Wilson v Oct 31 2003)
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CROSSREFS
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Sequence in context: A113717 A124563 A122704 this_sequence A000779 A053144 A089464
Adjacent sequences: A087544 A087545 A087546 this_sequence A087548 A087549 A087550
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Oct 24 2003
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EXTENSIONS
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More terms from njas, Oct 30 2003
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