OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
LINKS
Harry J. Smith, Table of n, a(n) for n=1..2000
Steven R. Finch, Digital Search Tree Constants [Broken link]
Steven R. Finch, Digital Search Tree Constants [From the Wayback machine]
Igor Pak, Greta Panova, and Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. [p. 13]
Jonathan Sondow and Eric W. Weisstein, MathWorld: Wallis Formula.
FORMULA
Equals Sum_{n>=0} 1/A002884(n)*Product_{j=1..n} 2^n/(2^n-1). - Geoffrey Critzer, Jun 30 2017
Equals 1/QPochhammer(1/2, 1/2)_{infinity}. - G. C. Greubel, Jan 18 2018
Equals 1 + Sum_{n>=1} 2^(n*(n-1)/2)/((2-1)*(2^2-1)*...*(2^n-1)). - Robert FERREOL, Feb 22 2020
Equals 1 / A048651 (constant). - Hugo Pfoertner, Nov 28 2020
Equals Sum_{n>=0} A000041(n)/2^n. - Amiram Eldar, Jan 19 2021
EXAMPLE
3.46274661945506361153795734292443116454075790290...
MAPLE
evalf(1+sum(2^(n*(n-1)/2)/product(2^k-1, k=1..n), n=1..infinity), 120); # Robert FERREOL, Feb 22 2020
MATHEMATICA
N[ Product[ 1/(1 - 1/2^k), {k, 1, Infinity} ], 500 ]
RealDigits[1/QPochhammer[1/2, 1/2], 10, 100][[1]] (* Vaclav Kotesovec, Jun 22 2014 *)
PROG
(PARI) { default(realprecision, 2080); x=prodinf(k=1, 1/(1 - 1/2^k)); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065446.txt", n, " ", d)) } \\ Harry J. Smith, Oct 19 2009
(PARI) prodinf(k=1, 1/(1-1/2^k)) \\ Michel Marcus, Feb 22 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Nov 18 2001
EXTENSIONS
More terms from Robert G. Wilson v, Nov 19 2001
Further terms from Vladeta Jovovic, Dec 01 2001
STATUS
approved