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 A090763 a(n) = (3*n+3)!/(3*n!*(2*n+2)!). 1
 1, 10, 84, 660, 5005, 37128, 271320, 1961256, 14060475, 100150050, 709634640, 5006710800, 35197176924, 246681069040, 1724337127920, 12025860872784, 83702724824775, 581558091471630, 4034231805704100, 27945630038703300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). LINKS FORMULA 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] EXAMPLE E.g. a(3)=660. MAPLE 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 MATHEMATICA 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] PROG (Sage) [binomial(3*n, n)*n/3 for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009] CROSSREFS Sequence in context: A014831 A048440 A092718 * A016131 A027310 A155593 Adjacent sequences:  A090760 A090761 A090762 * A090764 A090765 A090766 KEYWORD nonn,changed AUTHOR Al Hakanson (hawkuu(AT)excite.com), Feb 15 2004 EXTENSIONS More terms from Robert G. Wilson v Feb 18 2004 Simpler description from Vladeta Jovovic, Feb 22 2004 STATUS approved

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