OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
StackExchange, Improving bound on sqrt(2*sqrt(3*sqrt4*...)))
Eric Weisstein's MathWorld, Somos's Quadratic Recurrence Constant
FORMULA
Equals A112302^2.
Equals exp( Sum_{n>=1} log(n)/2^(n-1) ).
Also equals exp(-2*PolyLog'(0,1/2)), where PolyLog' is the derivative of PolyLog(n,x) w.r.t. n.
EXAMPLE
2.7612068419574980332304546465801311048761259807153...
MATHEMATICA
RealDigits[Exp[-2*Derivative[1, 0][PolyLog][0, 1/2]], 10, 102] // First
RealDigits[Exp[2*Sum[(1/2)^n*Log[n], {n, 2, 2000}]], 10, 100][[1]] (* G. C. Greubel, Sep 30 2018 *)
PROG
(PARI) exp(sumpos(n=1, log(n+1)/2^n)) \\ Charles R Greathouse IV, Apr 18 2016
(Magma) SetDefaultRealField(RealField(100)); Exp(2*(&+[(1/2)^n*Log(n): n in [2..2000]])); // G. C. Greubel, Sep 30 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 22 2015
STATUS
approved