A086308 Decimal expansion of Otter's asymptotic constant beta for the number of unrooted trees.

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

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