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copied!<p>Notice that WolframAlpha returns a "Decimal Approximation". If you don't need absolute precision, you could do the same thing by calculating the factorials with <a href="http://en.wikipedia.org/wiki/Stirling%27s_approximation" rel="nofollow noreferrer">Stirling's Approximation</a>.</p> <p>Now, Stirling's approximation requires the evaluation of (n/e)^n, where e is the base of the natural logarithm, which will be by far the slowest operation. But this can be done using the techniques outlined in <a href="https://stackoverflow.com/questions/101439/the-most-efficient-way-to-implement-an-integer-based-power-function-powint-int/163572#163572">another stackoverflow post</a>.</p> <p>If you use double precision and repeated squaring to accomplish the exponentiation, the operations will be:</p> <ul> <li>3 evaluations of a Stirling approximation, each requiring O(log n) multiplications and one square root evaluation.</li> <li>2 multiplications</li> <li>1 divisions</li> </ul> <p>The number of operations could probably be reduced with a bit of cleverness, but the total time complexity is going to be O(log n) with this approach. Pretty manageable.</p> <p>EDIT: There's also bound to be a lot of academic literature on this topic, given how common this calculation is. A good university library could help you track it down.</p> <p>EDIT2: Also, as pointed out in another response, the values will easily overflow a double, so a floating point type with very extended precision will need to be used for even moderately large values of k and n.</p>

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