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A341491
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a(n) = binomial(6*n, n) * hypergeom([-5*n, -n], [-6*n], -1).
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5
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1, 11, 221, 4991, 118721, 2908411, 72616013, 1837271615, 46943003137, 1208483403179, 31297149356221, 814471993937855, 21281058718583873, 557930580979801755, 14669716953106628781, 386675596518995000191, 10214494658006725840897, 270345191656309313382475
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OFFSET
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0,2
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COMMENTS
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In general, for k > 1, binomial(k*n, n) * hypergeom([(1-k)*n, -n], [-k*n], -1) ~ sqrt((k + (k^2 - k + 1) / sqrt(k^2 - 2*k + 2)) / (4*(k-1)*Pi*n)) * ((A341476(k) + A341477(k)*sqrt((k-1)^2 + 1)) / (k-1)^(k-1))^n.
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LINKS
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FORMULA
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a(n) ~ sqrt((6 + 31/sqrt(26))/(20*Pi*n)) * (42671 + 8346*sqrt(26))^n / 5^(5*n).
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MATHEMATICA
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Table[Binomial[6*n, n] * Hypergeometric2F1[-5*n, -n, -6*n, -1], {n, 0, 20}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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