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Search: id:A090763
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| A090763 |
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a(n) = (3*n+3)!/(3*n!*(2*n+2)!). |
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+0
2
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| 1, 10, 84, 660, 5005, 37128, 271320, 1961256, 14060475, 100150050, 709634640, 5006710800, 35197176924, 246681069040, 1724337127920, 12025860872784, 83702724824775, 581558091471630, 4034231805704100, 27945630038703300
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=1/(integral_{x=0 to 1}(x^(2/3)-x)^n dx).
The same sequence is produced by a(n)=1/(integral_{x=0 to 1}(x-x^1.5)^n dx).
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FORMULA
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a:=n->sum(j*binomial(n,j)*binomial(2*(n-1),j)/6,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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EXAMPLE
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E.g. a(3)=660.
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MAPLE
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a:=n->sum(j*binomial(n, j)*binomial(2*(n-1), j)/6, j=0..n): seq(a(n), n=2..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006
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MATHEMATICA
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a[n_] := 1/Integrate[(x^(2/3) - x)^n, {x, 0, 1}]; Table[ a[n], {n, 0, 19}] (from Robert G. Wilson v Feb 18 2004)
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CROSSREFS
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Sequence in context: A014831 A048440 A092718 this_sequence A016131 A027310 A104128
Adjacent sequences: A090760 A090761 A090762 this_sequence A090764 A090765 A090766
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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), Feb 15 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) Feb 18 2004
Simpler description from Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 22 2004
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