Polynomials of Fibonacci numbers (noch nicht übersetzt)

Problem 435

The Fibonacci numbers {fn,n0} are defined recursively as fn=fn1+fn2 with base cases f0=0 and f1=1.

Define the polynomials {Fn,n0} as Fn(x)=ni=0fixi.

For example, F7(x)=x+x2+2x3+3x4+5x5+8x6+13x7, and F7(11)=268357683.

Let n=1015. Find the sum 100x=0Fn(x) and give your answer modulo 1307674368000 (=15!).