Polynomials of Fibonacci numbers (noch nicht übersetzt)
Problem 435
The Fibonacci numbers {fn,n≥0} are defined recursively as fn=fn−1+fn−2 with base cases f0=0 and f1=1.
Define the polynomials {Fn,n≥0} as Fn(x)=n∑i=0fixi.
For example, F7(x)=x+x2+2x3+3x4+5x5+8x6+13x7, and F7(11)=268357683.
Let n=1015. Find the sum 100∑x=0Fn(x) and give your answer modulo 1307674368000 (=15!).