Distribution of time to return for symmetric random walks

Question

Let $X_k$ be $1$ or $-1$ with equal probability $\frac{1}{2}$ if $k > 0$, and $S_n = X_1 + \dots + X_n$. We start at $S_0 = 0$. If $T$ is the time (number of steps) to first return to zero (that is, the first $t>0$ such that $S_t=0$), what is the probability $P(T = t)$, for $t = 2, 4, 6$ and so on? The expectation of $T$ is known to be infinite.