This seems quite hard. Start by noticing that is the coefficient of in .

Therefore is the coefficient of in .

But (writing the terms in reverse order) (sum of geometric series), and this simplifies to . The coefficient of in that expression is the sum of all the binomial coefficients of powers of x in minus the sum of the coefficients in the first half of the expansion of .

But the sum of all the binomial coefficients of powers of x in is . Also, the symmetry of the binomial coefficients (the fact that ) means that the sum of the coefficients in the first half of the expansion of is .

Therefore .