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 A086308 Decimal expansion of Otter's asymptotic constant beta for the number of unrooted trees. 7
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A000055(n) ~ 0.5349496061 * alpha^n * n^(-5/2), where alpha = 2.95576528565199497... (see A051491). - Vaclav Kotesovec, Jan 04 2013 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6., p. 296. LINKS Table of n, a(n) for n=0..105. Eric Weisstein's World of Mathematics, Tree EXAMPLE 0.53494960614230701455037971105206839814311651405699... MATHEMATICA 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 *) CROSSREFS Cf. A000055, A000081, A051491, A187770. Sequence in context: A109681 A196406 A070367 * A229943 A198132 A117967 Adjacent sequences: A086305 A086306 A086307 * A086309 A086310 A086311 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jul 15 2003 EXTENSIONS Corrected and extended by Vaclav Kotesovec, Jan 04 2013 More terms from Vaclav Kotesovec, Jun 20 2013 and Dec 26 2020 STATUS approved

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Last modified May 22 13:22 EDT 2024. Contains 372755 sequences. (Running on oeis4.)