OFFSET
0,1
COMMENTS
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)
Amirmohammad Farzaneh, Mihai-Alin Badiu, and Justin P. Coon, On Random Tree Structures, Their Entropy, and Compression, arXiv:2309.09779 [cs.IT], 2023.
Eric Weisstein's World of Mathematics, Rooted Tree
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
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jan 04 2013
STATUS
approved