In 1972. D.A. Branna conjectured that all of the odd coefficients,a2n+1of the power series (1+xz)α/(1-z) were dominated by those of the series (1 +z)α(1-z) for the parameter range 0 < α < 1 after having shown that this was not true for the even coefficients. He verified the case when 2n+ 1 = 3 The case when 2n+ 1 = 5 was verified in the mid-eighties by J. G. Milcetich. In this paper, we verify the case when 2n+ l = 7 using classical Sturm sequence arguments and some computer algebra.