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A188686
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Binomial transform of the sequence of binomial(3n,n).
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12
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1, 4, 22, 139, 934, 6484, 45931, 329893, 2393470, 17499892, 128732992, 951674398, 7064138779, 52616241370, 393052285291, 2943582912904, 22093111508686, 166141033332448, 1251528633163264, 9442096410241438, 71333250226656784
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: 2*cos((1/3)*arcsin(3/2*sqrt(3x/(1-x))))/sqrt(4-35x+31x^2).
D-finite recurrence: 2*n*(2*n-1)*a(n) = (39*n^2-43*n+12)*a(n-1) - 2*(n-1)*(33*n-34)*a(n-2) + 31*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Oct 20 2012
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MATHEMATICA
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Table[Sum[Binomial[n, k]Binomial[3k, k], {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), k, 0, n), n, 0, 20);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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