OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.5 Kalmar's composition constant, p. 294.
LINKS
Philippe Flajolet and Helmut Prodinger, Level number sequences for trees.
FORMULA
EXAMPLE
0.254505523565319513370881770031546156046493741725...
MATHEMATICA
digits = 105; m0 = 5; dm = 2; Clear[f, g, v, K]; v[c_, d_] := v[c, d] = If[d<0 || c<0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2*c}]]]; H[n_] := v[1, n]; H[1] = 1; f[x_, m_] := Sum[((-1)^(j+1)*x^(2^(j+1)-2-j))/Product[1-x^(2^k-1), {k, 1, j}], {j, 1, m}] // N[#, digits]&; g[m_] := g[m] = (1/x /. FindRoot[f[x, m] == 1, {x, 5/9, 4/9, 6/9}, WorkingPrecision -> digits]); g[m0]; g[m = m0+dm]; While[RealDigits[g[m], 10, digits+5] != RealDigits[g[m-dm], 10, digits+5], m = m+dm]; nu = g[m]; K[m_] := K[m] = H[m]/nu^m; dm=100; K[m = 100]; K[m = m+dm]; While[Print[m]; RealDigits[K[m], 10, digits+5] != RealDigits[K[m-dm], 10, digits+5], m = m+dm]; RealDigits[K[m], 10, digits-5] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jan 12 2015
STATUS
approved