OFFSET
1,1
COMMENTS
alpha is used to measure the expected height of random binary search trees.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.13 Binary search tree constants, p. 352.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Luc Devroye, A note on the height of binary search trees, Journal of the ACM, Vol. 33, No. 3 (1986), pp. 489-498.
Bruce Reed, The height of a random binary search tree, J. ACM, 50 (2003), 306-332.
John Michael Robson, The height of binary search trees, Australian Computer Journal, Vol. 11, No. 4 (1979), pp. 151-153. [broken link]
Larry Shepp, Doron Zeilberger and Cun-Hui Zhang, Pick up sticks, arXiv preprint arXiv:1210.5642 [math.CO] (2012).
Wikipedia, Binary search tree
FORMULA
EXAMPLE
4.31107040700100503504707609644689027839156299804028805066937...
MAPLE
alpha:= solve(alpha*log((2*exp(1))/alpha)=1, alpha):
as:= convert(evalf(alpha/10, 130), string):
seq(parse(as[n+1]), n=1..120);
MATHEMATICA
RealDigits[ -1/ProductLog[-1/(2*E)] , 10, 105] // First (* Jean-François Alcover, Feb 19 2013 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Sep 21 2011
STATUS
approved