Characters of the symmetric group corresponding to partitions into two parts

Question

Let $n\in\mathbb N$ be a natural number and $\lambda=(a,b)\vdash n$ a partition of $n$ into two parts, i.e. $a\ge b$ and $a+b=n$. In this special case, is there a simple description of the character $\chi_\lambda$ of the irreducible $S_n$-representation corresponding to $\lambda$? I have tried to deduce something from the Frobenius character formula and also using the Murnaghan-Nakayama recursion, but so far I couldn't really come up with a simple description. I would really appreciate any references/theorems in that direction.