What will be the $n^{th}$ term of this given series? Given series is:
$$1+\frac{1\times x^2}{2\times 4}+\frac{1\times 3\times 5\times x^4}{2\times 4\times 6\times 8}+\frac{1\times 3\times 5\times 7\times 9\times x^6}{2\times 4\times 6\times 8\times 10\times 12}+.....\infty$$
I need to find it's $n^{th}$ term but am having trouble in dealing with increasing number of multiples in each step. Kindly Guide in How to proceed

$$a_0=1, \quad \text{and }a_n=\frac{x^{2n}}{2}\left(\prod_{k=0}^{n-1} \frac{2k+1}{2k+4}\right) \text{ for } n\ge1.$$
