Infinite product

I am actually trying to calculate a probability and hitting upon the infinite product:

[tex]\prod_{j=1}^{\infty}\frac{2^{j}-1}{2^{j}}[/tex]

Any idea what this might be (it's about 0.28, but I want the formula).
 

CRGreathouse

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I am actually trying to calculate a probability
that a binary matrix is nonsingular?

http://www.research.att.com/~njas/sequences/A048651 [Broken] is the constant. There are several formulas there, but probably none that are 'the formula' you hoped to find.
 
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