id	title	challengeType	forumTopicId	dashedName
5900f5201000cf542c510032	Problem 435: Polynomials of Fibonacci numbers	5	302106	problem-435-polynomials-of-fibonacci-numbers

--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);

function polynomialsOfFibonacciNumbers() {

  return true;
}

polynomialsOfFibonacciNumbers();

// solution required