Math Forum Discussions

denis

Posts: 1
Registered: 8/7/09

sums of different binomial coefficients
Posted: Aug 7, 2009 5:47 AM

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Hello,
I search a way to compute these sums :
k = Sum[C(K(i),i),{i, p, 1}]
where K(i) is a list like this :
K(p) = n
K(p-1) = K(p)-2
K(p-2) = K(p-1)-1
K(p-3) = n(p-2)-3
...
it's always decrementing but with arbitrary value
n is a number ~10^10 (and greater)
p is not greater as n/2

I search a way to compute it quickly.
for n ~10^9 i have a way to compute it in 6 minutes
but for n ~10^10 it takes me 15 hours...

Is there a way to rewrite the sums perhaps in a way it will be faster to calculate ?

my usage is to calculate the combinadic on files greater than 1Mo.

Thanks by advance for your suggestions.