Where's my Gamma!

By Legendre Duplication Formula :

$\left( n+\frac { 1 }{ 2 } \right) !=\frac { \sqrt { \pi } (2n+2)! }{ { 4 }^{ n+1 }(n+1)! }$

$3.5! = \left( 3+\frac { 1 }{ 2 } \right) !=\frac { \sqrt { \pi } (8)! }{ { 4 }^{ 3+1 }(4!) } \approx 11.63$

$OR$ $\left( \frac { 7 }{ 2 } \right) !=\quad \frac { 7 }{ 2 } .\frac { 5 }{ 2 } .\frac { 3 }{ 2 } .\left( \frac { 1 }{ 2 } \right) !=\quad \left( \frac { 105 }{ 8 } \right) \left( \frac { 1 }{ 2 } \right) \Gamma \left( \frac { 1 }{ 2 } \right) =\quad \frac { 105\sqrt { \pi } }{ 16 } \approx 11.63$