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.