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

10^{10}, and ans is to be found MODULUS to some prime number..like

10^{10}+7).

Please simplify the series if possible or let me know the way how to

solve it efficiently.