# Problem 435: Polynomials of Fibonacci numbers
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) = ∑fixi for 0 ≤ i ≤ n. For example, F7(x) = x + x2 + 2x3 +
3x4 + 5x5 + 8x6 + 13x7, and F7(11) = 268357683. Let n = 1015. Find the
sum \[∑0≤x≤100 Fn(x)\] mod 1307674368000 (= 15!).