设\(M\subseteq {{N}^{+}}\),正项数列\(\{{{a}_{n}}\}\)的前\(n\)项的积为\({{T}_{n}}\),且\(\forall k\in M\),当\(n > k \)时,\(\sqrt{{{T}_{n+k}}{{T}_{n-k}}}={{T}_{n}}{{T}_{k}}\)都成立.
\((1)\)若\(M=\{1\}\),\({{a}_{1}}=\sqrt{3}\),\({{a}_{2}}=3\sqrt{3}\),求数列\(\{{{a}_{n}}\}\)的前\(n\)项和;
\((2)\)若\(M=\{3,4\}\),\({{a}_{1}}=\sqrt{2}\),求数列\(\{{{a}_{n}}\}\)的通项公式.