Perhaps the most famous recursive sequence is the Fibonacci sequence. There is even an international Fibonacci society that meets annually in different cities around the globe. Consecutive terms can be found in the measure of index cards and seeds on a sunflower. The ratio of two consecutive terms approaches the golden mean, associated with the golden rectangle. The sequence is defined as follows:
a 0 = 1, a 1 = 1, a k = a k-2 + a k-1, where k≥2.
Write the first 15 terms of the sequence.
Find the first five terms of the sequence an = (xn - 1) / (n+1)!