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A066802
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Binomial(6*n,3*n).
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4
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20, 924, 48620, 2704156, 155117520, 9075135300, 538257874440, 32247603683100, 1946939425648112, 118264581564861424, 7219428434016265740, 442512540276836779204, 27217014869199032015600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For the trisection of a sequence (here A000984) given by its real o.g.f. see a comment and a reference under A187357.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
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FORMULA
| a(n)=sum_{0<=i, j, k<=n} binomial(n, i)*binomial(n, j)*binomial(n, k)*binomial(3n, i+j+k) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 08 2005
O.g.f.(with a(0):=1): (cb(x^(1/3)) + sqrt(2)*P(x^(1/3))*sqrt(1/P(x^(1/3))+1+2*x^(1/3)))/3, with cb(x):=1/sqrt(1-4*x) (o.g.f. of A000984) and P(x):=P(-1/2,4*x)= 1/sqrt(1+4*x+16*x^2) (o.g.f. of A116091, with P(x,z) the o.g.f. of the Legendre polynomials). W. Lang, (wolfdieter.lang(AT)kit.edu) Mar 24 2011.
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PROG
| (PARI) { for (n=1, 100, write("b066802.txt", n, " ", binomial(6*n, 3*n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 28 2010]
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CROSSREFS
| A187364 binomial(2(3n+1),3n+1)/2, A187365 binomial(2(3n+2),3n+2)/3!.
Sequence in context: A117798 A006424 A113102 * A066798 A072035 A069578
Adjacent sequences: A066799 A066800 A066801 * A066803 A066804 A066805
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 18 2002
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