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Search: id:A094075
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| A094075 |
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Denominator of I(n)=integral_{x=0 to 1/n}(x^2-1)^3 dx. |
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+0
1
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| 105, 13440, 229635, 1720320, 8203125, 29393280, 86472015, 220200960, 502211745, 1050000000, 2046152955, 3762339840, 6588594285, 11068417920, 17940234375, 28185722880, 43085560665, 64283103360, 93856532595, 134400000000
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The numerator is b(n)=-105*n^6+105*n4-63*n^2+15. E.g. b(3)=-68392.
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FORMULA
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a(n)=105*n^7=105*A001015.
G.f.: 105*x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^8 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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EXAMPLE
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E.g. I(3)= -68592/229635.
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MATHEMATICA
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f[n_] := Integrate[(x^2 - 1)^3, {x, 0, 1/n}]; Table[(-105n^6 + 105n^4 - 63n^2 + 15)/f[n], {n, 20}] (from Robert G. Wilson v May 03 2004)
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CROSSREFS
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Sequence in context: A165055 A075914 A075924 this_sequence A018233 A082368 A001546
Adjacent sequences: A094072 A094073 A094074 this_sequence A094076 A094077 A094078
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Apr 29 2004
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 3 2004
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