# Math Help - Reduce the sequence..or how to calculate it efficiently

1. ## Reduce the sequence..or how to calculate it efficiently

Sequence is
(in Summation notation)
SUMMATION[from k=0 to k=floor(n/2)] (n-k)C(k) * 2(n-k-1)
refer to this image
http://i.snag.gy/tFI7e.jpg
after expanding it becomes
(n)C(0)*2(n-1) + (n-1)C(1)*2(n-2) + (n-2)C(2) * 2(n-3) +....

I want to calculate the value of function for a large value of n(up to
1010, and ans is to be found MODULUS to some prime number..like
1010+7).

Please simplify the series if possible or let me know the way how to
solve it efficiently.