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A370293
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Decimal expansion of a constant related to the asymptotics of A229452.
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5
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4, 9, 0, 1, 5, 2, 8, 1, 2, 2, 2, 8, 9, 7, 8, 7, 3, 0, 4, 7, 7, 8, 0, 1, 2, 8, 8, 9, 1, 6, 1, 0, 4, 9, 5, 5, 5, 3, 6, 6, 1, 6, 4, 0, 2, 1, 4, 0, 1, 2, 7, 3, 1, 0, 5, 2, 5, 1, 4, 8, 9, 7, 8, 3, 7, 1, 9, 9, 3, 2, 5, 2, 4, 2, 1, 6, 8, 9, 9, 3, 9, 7, 2, 2, 7, 8, 0, 4, 4, 2, 6, 7, 3, 1, 4, 0, 1, 6, 3, 9, 2, 9, 8, 3, 5, 4, 9
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OFFSET
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-1,1
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COMMENTS
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In general, for m >= 1, if g.f. = exp(m * Sum_{n>=1} (3*n)!/(3!*n!^3) * x^n/n ), then a(n) ~ m * 2^(2*m-2) * 3^((m-1)/2) * Pi^(m-1) * A370293^m * 3^(3*n) / n^2, cf. A229452 (m=1), A370289 (m=2), A370288 (m=3), A229451 (m=6).
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LINKS
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FORMULA
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Equals limit_{n->oo} A229452(n) / (3^(3*n)/n^2).
Equals limit_{n->oo} (A370288(n) * n^2 / (144 * Pi^2 * 3^(3*n)))^(1/3).
Equals limit_{n->oo} (A370289(n) * n^2 / (8 * 3^(1/2) * Pi * 3^(3*n)))^(1/2).
Equals limit_{n->oo} (A229451(n) * n^2 / (2^11 * 3^(7/2) * Pi^5 * 3^(3*n)))^(1/6).
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EXAMPLE
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0.0490152812...
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MATHEMATICA
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RealDigits[E^(HypergeometricPFQ[{1, 1, 4/3, 5/3}, {2, 2, 2}, 1]/27) / (4*Sqrt[3]*Pi), 10, 120][[1]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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