  In this paper, we investigate two methods to express the natural powers of
$2$ as sums over integer partitions. First we consider a formula by N. J. Fine
that allows us to express a binomial coefficient in terms of multinomial
coefficients as a sum over partitions. The second method invokes the central
binomial coefficients and the logarithmic differentiation of their generating
function. Some experimental results suggest the existence of other methods of
decomposing the power of $2$ as sums over partitions.
