OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.13 Binary search tree constants, p. 356.
LINKS
Eric Weisstein's World of Mathematics, Tree Searching
FORMULA
Equals Sum_{k>=1} k*2^(k*(k-1)/2)*(Sum_{j=1..k} 1/(2^j-1))/Product_{j=1..k} (2^j-1).
EXAMPLE
7.743131985536896591446283856749784...
MAPLE
theta:= sum((((k*2^(k*(k-1)/2)) *sum(1/(2^j-1), j=1..k))/
product(2^j-1, j=1..k)), k=1..infinity):
s:= convert(evalf(theta, 110), string):
map(parse, subs("."=[][], [seq(i, i=s)]))[]; # Alois P. Heinz, Jun 27 2014
MATHEMATICA
digits = 102; m0 = 100; dm = 100; Clear[theta]; theta[m_] := theta[m] = Sum[((k*2^(k*((k-1)/2)))*Sum[1/(2^j-1), {j, 1, k}])/Product[2^j-1, {j, 1, k}], {k, 1, m}] // N[#, digits+10]&; theta[m0]; theta[m = m0 + dm]; While[RealDigits[theta[m], 10, digits+10] != RealDigits[theta[m - dm], 10, digits+10], Print["m = ", m]; m = m + dm]; RealDigits[theta[m], 10, digits] // First (* Jean-François Alcover, Jun 27 2014 *)
digits = 102; theta = NSum[((k*2^(k*((k-1)/2)))*((QPolyGamma[0, 1+k, 1/2] - QPolyGamma[0, 1, 1/2])/Log[2]))/((-1)^k*QPochhammer[2, 2, k]), {k, 1, Infinity}, WorkingPrecision -> digits+5, NSumTerms -> 3*digits]; RealDigits[theta, 10, digits] // First (* Jean-François Alcover, Nov 19 2015 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 15 2003
STATUS
approved