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Search: id:A145921
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| A145921 |
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Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function. |
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+0
1
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| 1, 8, 81, 2048, 15625, 6718464, 5764801, 2147483648, 31381059609, 64000000000000, 3138428376721, 2218611106740436992, 3937376385699289, 1115112108958398021632, 39903080760955810546875
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OFFSET
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1,2
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COMMENT
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n*B(n,1+1/n) = Gamma(n+1)*Gamma(1+1/n)/Gamma(1+n+1/n) is the integral over F(n)=[1-x^(1/n)]^(1/n) from x=0 to 1.
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EXAMPLE
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The fractions are 1/2, 8/15, 81/140, 2048/3315, 15625/24024, ...
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MAPLE
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seq( numer(n*Beta(n, 1+1/n)), n=1..30) ;
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PROGRAM
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(DERIVE) VECTOR(NUMERATOR(F(n)), n, 1, 10)
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CROSSREFS
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Sequence in context: A022519 A138439 A026845 this_sequence A100399 A022504 A104126
Adjacent sequences: A145918 A145919 A145920 this_sequence A145922 A145923 A145924
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KEYWORD
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nonn,frac
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AUTHOR
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Jose Luis (jl_altamirano(AT)yahoo.com), Oct 25 2008
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EXTENSIONS
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Definition clarified by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2008
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