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A086318
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Decimal expansion of asymptotic constant eta for counts of weakly binary trees.
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4
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7, 9, 1, 6, 0, 3, 1, 8, 3, 5, 7, 7, 5, 1, 1, 8, 0, 7, 8, 2, 3, 6, 2, 8, 4, 5, 5, 7, 2, 3, 2, 6, 8, 2, 2, 4, 0, 7, 1, 7, 4, 2, 4, 1, 8, 0, 9, 0, 7, 8, 9, 4, 6, 7, 3, 1, 2, 3, 0, 7, 8, 3, 0, 9, 9, 2, 2, 9, 0, 4, 4, 1, 5, 0, 3, 8, 9, 3, 2, 9, 2, 5, 5, 4, 4, 6, 6, 7, 9, 0, 8, 6, 8, 4, 0, 4, 6, 3, 0, 3, 8, 3
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text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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EXAMPLE
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0.791603183577511807823628455723268224071742418090789...
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MATHEMATICA
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digits = 102; c[0] = 2; c[n_] := c[n] = c[n - 1]^2 + 2; eta[n_Integer] := eta[n] = 1/2 * Sqrt[c[n]^2^(-n)/Pi] * Sqrt[3 + Sum[1/Product[c[j], {j, 1, k}], {k, 1, n}]]; eta[5]; eta[n = 10]; While[RealDigits[eta[n], 10, digits] != RealDigits[eta[n - 5], 10, digits], n = n + 5]; RealDigits[eta[n], 10, digits] // First (* Jean-François Alcover, May 27 2014 *)
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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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