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Search: id:A088505
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| A088505 |
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a(n)=(2^(3*n-1))/(integral_{x = 0 to 1} (1-x^4)^n dx). |
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+0
1
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| 5, 45, 390, 3315, 27846, 232050, 1922700, 15862275, 130423150, 1069469830, 8750207700, 71460029550, 582674087100, 4744631852100, 38589672397080, 313541088226275, 2545215892660350, 20644528907133950, 167329339563085700
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OFFSET
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1,1
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FORMULA
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The integral is equal to n!*Pi*sqrt(2)/(4*GAMMA(3/4)*GAMMA(n+5/4)). - N. J. A. Sloane (njas(AT)research.att.com).
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EXAMPLE
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a(3)=390 (a(0) would be 1/2, so the sequence begins at n=1).
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MATHEMATICA
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f[n_] := 2^(3n - 1)/Integrate[(1 - x^4)^n, {x, 0, 1}]; Table[ f[n], {n, 1, 19}] (from Robert G. Wilson v Feb 26 2004)
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PROGRAM
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(PARI) a(n)=round(2^(3*n-1)/(n!*Pi*sqrt(2)/(4*gamma(3/4)*gamma(n+5/4))))
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CROSSREFS
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Sequence in context: A043025 A125836 A001260 this_sequence A067403 A022022 A058410
Adjacent sequences: A088502 A088503 A088504 this_sequence A088506 A088507 A088508
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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), Nov 13 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 14 2003
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