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 A187770 Decimal expansion of Otter's asymptotic constant beta for the number of rooted trees. 12
 4, 3, 9, 9, 2, 4, 0, 1, 2, 5, 7, 1, 0, 2, 5, 3, 0, 4, 0, 4, 0, 9, 0, 3, 3, 9, 1, 4, 3, 4, 5, 4, 4, 7, 6, 4, 7, 9, 8, 0, 8, 5, 4, 0, 7, 9, 4, 0, 1, 1, 9, 8, 5, 7, 6, 5, 3, 4, 9, 3, 5, 4, 5, 0, 2, 2, 6, 3, 5, 4, 0, 0, 4, 2, 0, 4, 7, 6, 4, 6, 0, 5, 3, 7, 9, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A000081(n) ~ 0.439924012571 * alpha^n * n^(-3/2), alpha = 2.95576528565199497... (see A051491) REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6., p.296 D. E. Knuth, Fundamental Algorithms, 3d Ed. 1997, p. 396. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1799, (this constant was computed by David Broadhurst in November 1999) Eric Weisstein's World of Mathematics, RootedTree EXAMPLE 0.43992401257102530404090339143454476479808540794... MATHEMATICA digits = 87; 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)]; RealDigits[b, 10, digits] // First (* Jean-François Alcover, Sep 24 2014 *) CROSSREFS Cf. A000081, A051491, A000055, A086308. Sequence in context: A275473 A131805 A197694 * A103218 A319311 A107381 Adjacent sequences:  A187767 A187768 A187769 * A187771 A187772 A187773 KEYWORD nonn,cons AUTHOR Vaclav Kotesovec, Jan 04 2013 STATUS approved

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Last modified October 18 16:27 EDT 2018. Contains 316323 sequences. (Running on oeis4.)