Dougall's Hypergeometric Theorem/Corollary 6

Corollary to Dougall's Hypergeometric Theorem
Let $\map \Re {n} < \dfrac 2 3$.

Then:


 * $\ds \map { {}_4 \operatorname F_3} { { {\dfrac n 2 + 1, n, n, n} \atop {\dfrac n 2, 1, 1} } \, \middle \vert \, -1} = \dfrac {\map \sin {\pi n} } {\pi n } $

Proof
Let $x = y = -n$ in Dougall's Hypergeometric Theorem: Corollary 3

Before substitution:

After substitution: