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A254157
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a(n) = binomial(3*n,n)^n.
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1
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1, 3, 225, 592704, 60037250625, 244217432431215243, 40928832685064366701940736, 287432029715751041166252933120000000, 85609985515193235253656684862285741981771256961, 1091210761769150876962680951989752349788052377750396728515625
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OFFSET
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0,2
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COMMENTS
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Generally, for p > 1 is
binomial(p*n,n) ~ (p^p/(p-1)^(p-1))^n * sqrt(p/(2*Pi*n*(p-1))) * (1 - (p^2-p+1)/(12*n*p*(p-1))).
binomial(p*n,n)^n ~ exp(-(p^2-p+1)/(12*p*(p-1))) * (p^p/(p-1)^(p-1))^(n^2) * (p/(2*Pi*n*(p-1)))^(n/2).
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LINKS
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FORMULA
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a(n) ~ exp(-7/72) * 3^(3*n^2 + n/2) / (2^(2*n^2 + n) * Pi^(n/2) * n^(n/2)).
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MATHEMATICA
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Table[Binomial[3n, n]^n, {n, 0, 10}]
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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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