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A243396
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Decimal expansion of 'etaHat', a constant used in the asymptotic evaluation of e.g.f. coefficients for the number of labeled mobiles.
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1
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4, 6, 5, 6, 3, 8, 6, 4, 6, 7, 7, 9, 0, 7, 5, 7, 3, 7, 1, 0, 9, 9, 7, 5, 9, 1, 0, 2, 6, 4, 2, 9, 0, 5, 7, 4, 6, 3, 2, 5, 5, 0, 1, 4, 6, 1, 7, 4, 3, 4, 8, 3, 8, 9, 3, 5, 6, 0, 0, 9, 9, 0, 1, 9, 1, 7, 6, 5, 1, 3, 9, 2, 6, 1, 0, 8, 8, 0, 4, 7, 7, 5, 6, 9, 3, 4, 0, 6, 6, 6, 1, 8, 9, 8, 4, 9, 7, 3, 8, 8, 6, 1, 5, 9
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.
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LINKS
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FORMULA
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A038037 = Numerator of n-th coefficient ~ etaHat * xiHat^n * n^(n-1), where xiHat is A243395.
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EXAMPLE
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0.46563864677907573710997591026429...
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MATHEMATICA
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digits = 104; mu = x /. FindRoot[x/(1 - x) == 1 + Log[1/(1 - x)], {x, 1/2}, WorkingPrecision -> digits + 5] ; etaHat = Sqrt[mu*(1 - mu)]; RealDigits[etaHat, 10, digits] // First
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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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