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A090763
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a(n) = (3*n+3)!/(3*n!*(2*n+2)!).
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1
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1, 10, 84, 660, 5005, 37128, 271320, 1961256, 14060475, 100150050, 709634640, 5006710800, 35197176924, 246681069040, 1724337127920, 12025860872784, 83702724824775, 581558091471630, 4034231805704100, 27945630038703300
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OFFSET
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0,2
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COMMENTS
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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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LINKS
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Table of n, a(n) for n=0..19.
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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
a(n)=1/(2*Beta(2n,n)) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), May 17 2009]
a(1)=1; a(n)=a(n-1)*2*binomial(3n,3)/binomial(2n,3) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), May 19 2009]
a(n)=1/2*Sum{j=1,n}(j*binomial(2n,j)*binomial(n,j)) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), May 22 2009]
a(n)=(n+1)*A025174(n+1). [From R. J. Mathar, Jun 21 2009]
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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)
a[n_] := 1/(2*Beta[2n, n]) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), May 17 2009]
a[n_]:=1/2*Sum[j*Binomial[2 n, j]*Binomial[n, j], {j, 1, n}] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), May 22 2009]
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PROG
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(Sage) [binomial(3*n, n)*n/3 for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
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CROSSREFS
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Sequence in context: A014831 A048440 A092718 * A016131 A027310 A155593
Adjacent sequences: A090760 A090761 A090762 * A090764 A090765 A090766
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KEYWORD
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nonn,changed
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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 Feb 18 2004
Simpler description from Vladeta Jovovic, Feb 22 2004
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STATUS
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approved
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