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A188912
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Binomial convolution of the binomial coefficients bin(3n,n)/(2n+1) (A001764).
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3
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1, 2, 8, 42, 260, 1816, 13962, 116094, 1029124, 9609144, 93569808, 942642696, 9763181946, 103455616400, 1117379189926, 12264816349938, 136501928050116, 1537591374945704, 17503603786398576, 201128739609458904, 2330480521265639136
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..93
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FORMULA
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a(n) = sum(binomial(n, k)*binomial(3*k, k)/(2*k+1)*binomial(3*n-3*k, n-k)/(2*n-2*k+1), k=0..n)
E.g.f: F(1/3,2/3;1,3/2;27*x/4)^2, where F(a1,a2;b1,b2;z) is a hypergeometric series.
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MATHEMATICA
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Table[Sum[Binomial[n, k]Binomial[3k, k]/(2k+1)Binomial[3n-3k, n-k]/(2n-2k+1), {k, 0, n}], {n, 0, 22}]
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PROG
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(Maxima) makelist(sum(binomial(n, k)*binomial(3*k, k)/(2*k+1)*binomial(3*n-3*k, n-k)/(2*n-2*k+1), k, 0, n), n, 0, 12);
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CROSSREFS
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Cf. A005809, A001764, A005809, A006256, A006013, A045721, A188911, A188913
Sequence in context: A013999 A130649 A054993 * A229285 A005315 A182520
Adjacent sequences: A188909 A188910 A188911 * A188913 A188914 A188915
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KEYWORD
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nonn,easy
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AUTHOR
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Emanuele Munarini, Apr 13 2011
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STATUS
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approved
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