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Re: Inconsistent behavior?

• To: mathgroup at smc.vnet.net
• Subject: [mg87270] Re: Inconsistent behavior?
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Sun, 6 Apr 2008 06:42:27 -0400 (EDT)
• Organization: University of Bergen
• References: <ft7ggo$bs3$1@smc.vnet.net>

angela wrote:
> Binomial[n,4] yields
> 1/24 (-3+n) (-2+n) (-1+n) n
> 
> Binomial[n,5] yields
> 1/120 (-4+n) (-3+n) (-2+n) (-1+n) n
> 
> Binomial[n,6] yields
> Binomial[n,6]
> 
> Binomial[n,7] yields
> Binomial[n,7]
> 

As you increase the second argument, the expression is getting larger 
quickly.  Binomial[n, 100] /. n -> 101 can be computed much more quickly 
if Binomial[n, 100] is not expanded in terms of n before the value 101 
is substituted.  You can explicitly request symbolic expansion using 
FunctionExpand:

Binomial[n, 100] // FunctionExpand

Szabolcs