--description--

The Fibonacci numbers $\{f_n, n ≥ 0\}$ are defined recursively as $f_n = f_{n - 1} + f_{n - 2}$ with base cases $f_0 = 0$ and $f_1 = 1$.

Define the polynomials $\{F_n, n ≥ 0\}$ as $F_n(x) = \displaystyle\sum_{i = 0}^n f_ix^i$.

For example, $F_7(x) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + 13x^7$, and $F_7(11) = 268\,357\,683$.

Let $n = {10}^{15}$. Find the sum $\displaystyle\sum_{x = 0}^{100} F_n(x)$ and give your answer modulo $1\,307\,674\,368\,000 \, (= 15!)$.

--hints--

polynomialsOfFibonacciNumbers() should return 252541322550.

assert.strictEqual(polynomialsOfFibonacciNumbers(), 252541322550);

--seed--

--seed-contents--

function polynomialsOfFibonacciNumbers() {

  return true;
}

polynomialsOfFibonacciNumbers();

--solutions--

// solution required