The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A109681 A196406 A070367 * A229943 A198132 A117967
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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