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

--description--

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!).

--hints--

euler435() should return 252541322550.

assert.strictEqual(euler435(), 252541322550);

function euler435() {

  return true;
}

euler435();

// solution required