已知直线\(l_{n}\):\(y=x-\sqrt{2n}\)与圆\(C_{n}\):\(x\)\({\,\!}^{2}+\)\(y\)\({\,\!}^{2}=2\)\(a_{n}\)\(+\)\(n\)交于不同的两点\(A_{n}\),\(B_{n}\),\(n\)\(∈\)\(N\)\({\,\!}^{*}.\)数列\(\{\)\(a_{n}\)\(\}\)满足:\(a\)\({\,\!}_{1}=1\),\({{a}_{n+1}}=\dfrac{1}{4}|{{A}_{n}}{{B}_{n}}{{|}^{2}}\).
\((1)\)求数列\(\{\)\(a_{n}\)\(\}\)的通项公式\(a_{n}\);
\((2)\)若\({{b}_{n}}=\dfrac{n}{4{{a}_{n}}}\),求数列\(\{\)\(b_{n}\)\(\}\)的前\(n\)项和\(T_{n}\).