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 A240943 Decimal expansion of the radius of convergence of Wedderburn-Etherington numbers g.f. 2
 4, 0, 2, 6, 9, 7, 5, 0, 3, 6, 7, 1, 4, 4, 1, 2, 9, 0, 9, 6, 9, 0, 4, 5, 3, 4, 8, 6, 5, 1, 0, 8, 3, 8, 0, 3, 4, 1, 7, 5, 5, 6, 7, 2, 1, 6, 2, 4, 9, 7, 2, 6, 5, 9, 2, 9, 1, 0, 5, 3, 4, 6, 4, 6, 0, 7, 6, 4, 2, 7, 2, 8, 9, 6, 6, 5, 2, 4, 2, 5, 8, 4, 1, 6, 4, 1, 6, 0, 9, 6, 0, 2, 6, 2, 1, 7, 2, 0, 5, 9, 5, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 297. LINKS Nils Berglund, Christian Kuehn, Model Spaces of Regularity Structures for Space-Fractional SPDEs, Journal of Statistical Physics, Springer Verlag, 2017, 168 (2), pp.331-368; HAL Id : hal-01432157. Nicolas Broutin and Philippe Flajolet, The height of random binary unlabelled trees, arXiv:0807.2365 [math.CO], 2008. Eric Weisstein's World of Mathematics, Weakly binary tree FORMULA 1/A086317. EXAMPLE 0.4026975036714412909690453486510838034175567216249726592910534646... MATHEMATICA digits = 102; n0 = 50; dn = 50; Clear[rho]; rho[n_] := rho[n] = (Clear[c]; c[0] = 0; y[z_] = Sum[c[k]*z^k, {k, 0, n}]; eq[0] = Rest[ Thread[CoefficientList[(-2*z + 2*y[z] - y[z]^2 - y[z^2])/2, z] == 0]]; s[1] = First[Solve[First[eq[0]], c[1]]]; Do[eq[k-1] = Rest[eq[k-2]] /. s[k-1]; s[k] = First[Solve[First[eq[k-1]], c[k]]], {k, 2, n}]; z /. FindRoot[ 2*z + y[z^2] == 1 /. Flatten[Table[s[k], {k, 1, n}]], {z, 1/2}, WorkingPrecision -> digits+10]); rho[n0]; rho[n = n0 + dn]; While[RealDigits[rho[n], 10, digits] != RealDigits[rho[n - dn], 10, digits], Print["n = ", n]; n = n + dn]; RealDigits[rho[n], 10, digits] // First (* or, after A086317: *) Clear[c, xi]; c[0] = 2; c[n_] := c[n] = c[n-1]^2 + 2; xi[n_Integer] := xi[n] = c[n]^(2^-n); xi[5]; xi[n = 10]; While[RealDigits[xi[n], 10, digits] != RealDigits[xi[n-5], 10, digits], n = n+5]; RealDigits[1/xi[n], 10, digits] // First (* Jean-François Alcover, Aug 04 2014 *) CROSSREFS Cf. A001190, A086317. Sequence in context: A016679 A178903 A322259 * A271823 A011352 A275983 Adjacent sequences:  A240940 A240941 A240942 * A240944 A240945 A240946 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Aug 04 2014 STATUS approved

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Last modified December 18 09:25 EST 2018. Contains 318219 sequences. (Running on oeis4.)