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Search: id:A077745
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| A077745 |
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Numerator of integral_{x=1..2} (x^2-1)^n dx. |
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+0
2
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| 1, 4, 38, 582, 12354, 335730, 11127150, 435300390, 19633815810, 1003121039970, 57259773499950, 3611583223860150, 249441581246630850, 18723487284033181650, 1517668796159163197550, 132117536404977132759750
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OFFSET
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0,2
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COMMENT
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Denominator is (2n+1)!/(n! 2^n).
Note that these fractions are not reduced. The reduced fractions are 1, 4/3, 38/15, 194/35, 4118/315, 22382/693, 247270/3003, 1381906/6435, etc. and lead to a different sequence of numerators. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 24 2008]
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FORMULA
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(-1)^n*(2*n+1)!!*(2*hypergeom([1/2, -n], [3/2], 4)-hypergeom([1/2, -n], [3/2], 1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 05 2002
E.g.f.: (2/sqrt(1-6*x)-1)/(1+2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 2003
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EXAMPLE
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If n=3 the integral is 194/35, so a(3) = 7!/(3! 2^3) * 194/35 = 582.
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MATHEMATICA
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a[n_] := (2n+1)!/n!/2^n*Integrate[(x^2-1)^n, {x, 1, 2}]
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CROSSREFS
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Cf. A076729.
Sequence in context: A155859 A120974 A113664 this_sequence A138214 A138562 A096332
Adjacent sequences: A077742 A077743 A077744 this_sequence A077746 A077747 A077748
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KEYWORD
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frac,nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Dec 02 2002
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