The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086315 Decimal expansion of constant theta appearing in the expected number of pair of twin vacancies in a digital tree. 1
 7, 7, 4, 3, 1, 3, 1, 9, 8, 5, 5, 3, 6, 8, 9, 6, 5, 9, 1, 4, 4, 6, 2, 8, 3, 8, 5, 6, 7, 4, 9, 7, 8, 4, 2, 9, 5, 5, 9, 3, 6, 5, 2, 8, 2, 8, 4, 1, 8, 8, 0, 8, 8, 8, 8, 6, 6, 5, 1, 8, 5, 5, 9, 1, 8, 3, 8, 3, 2, 9, 9, 7, 1, 5, 1, 7, 6, 2, 9, 2, 9, 0, 1, 5, 1, 0, 9, 4, 3, 9, 0, 7, 9, 9, 5, 5, 4, 3, 5, 6, 7, 5 (list; constant; graph; refs; listen; history; text; internal format)
 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 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 Sequence in context: A265306 A198544 A247274 * A185577 A201517 A010513 Adjacent sequences:  A086312 A086313 A086314 * A086316 A086317 A086318 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jul 15 2003 STATUS approved

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

Last modified August 5 18:00 EDT 2021. Contains 346488 sequences. (Running on oeis4.)