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A086308
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Decimal expansion of Otter's asymptotic constant beta for the number of unrooted trees.
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7
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5, 3, 4, 9, 4, 9, 6, 0, 6, 1, 4, 2, 3, 0, 7, 0, 1, 4, 5, 5, 0, 3, 7, 9, 7, 1, 1, 0, 5, 2, 0, 6, 8, 3, 9, 8, 1, 4, 3, 1, 1, 6, 5, 1, 4, 0, 5, 6, 9, 9, 0, 0, 9, 3, 9, 7, 7, 0, 7, 6, 8, 1, 0, 2, 3, 7, 5, 2, 3, 2, 1, 7, 8, 8, 0, 6, 4, 0, 6, 7, 2, 3, 9, 7, 8, 3, 2, 6, 2, 2, 4, 1, 8, 5, 9, 1, 1, 0, 4, 4, 4, 6, 6, 9, 3, 7
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OFFSET
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0,1
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COMMENTS
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A000055(n) ~ 0.5349496061 * alpha^n * n^(-5/2), where alpha = 2.95576528565199497... (see A051491). - Vaclav Kotesovec, Jan 04 2013
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6., p. 296.
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LINKS
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Table of n, a(n) for n=0..105.
Eric Weisstein's World of Mathematics, Tree
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EXAMPLE
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0.53494960614230701455037971105206839814311651405699...
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MATHEMATICA
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digits = 86; max = 250; s[n_, k_] := s[n, k] = a[n+1-k] + If[n < 2*k, 0, s[n-k, k]]; a[1] = 1; a[n_] := a[n] = Sum[a[k]*s[n-1, k]*k, {k, 1, n-1}]/(n-1); A[x_] := Sum[a[k]*x^k, {k, 0, max}]; APrime[x_] := Sum[k*a[k]*x^(k-1), {k, 0, max}]; eq = Log[c] == 1 + Sum[A[c^-k]/k, {k, 2, max}]; alpha = c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits+5]; b = Sqrt[(1+Sum[APrime[alpha^-k]/alpha^k, {k, 2, max}])/(2*Pi)]; beta = 2*Pi*b^3; RealDigits[beta, 10, digits] // First (* Jean-François Alcover, Sep 24 2014 *)
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CROSSREFS
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Cf. A000055, A000081, A051491, A187770.
Sequence in context: A109681 A196406 A070367 * A229943 A198132 A117967
Adjacent sequences: A086305 A086306 A086307 * A086309 A086310 A086311
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KEYWORD
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nonn,cons
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AUTHOR
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Eric W. Weisstein, Jul 15 2003
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EXTENSIONS
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Corrected and extended by Vaclav Kotesovec, Jan 04 2013
More terms from Vaclav Kotesovec, Jun 20 2013 and Dec 26 2020
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STATUS
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approved
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