The Fibonacci numbers {f_n, n 0} are defined recursively as f_n = f_n-1 + f_n-2 with base cases f₀ = 0 and f₁ = 1.

Define the polynomials {F_n, n 0} as F_n(x) = f_ixⁱ 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 [_0x100 F_n(x)] mod 1307674368000 (= 15!).