\begin{array}{l}
a_1=1+\frac{\displaystyle 0\cdot(-1)\cdot(-2)\cdot(-3)\cdot(-4)}{\displaystyle 120}(m-6)=1\vspace{0.5em}\\
a_2=2+\frac{\displaystyle 1\cdot 0\cdot(-1)\cdot(-2)\cdot(-3)}{\displaystyle 120}(m-6)=2\vspace{0.5em}\\
a_3=3+\frac{\displaystyle 2\cdot 1\cdot 0\cdot(-1)\cdot(-2)}{\displaystyle 120}(m-6)=3\vspace{0.5em}\\
a_4=4+\frac{\displaystyle 3\cdot 2\cdot 1\cdot 0\cdot(-1)}{\displaystyle 120}(m-6)=4,\vspace{0.5em}\\
a_5=5+\frac{\displaystyle 4\cdot 3\cdot 2\cdot 1\cdot 0}{\displaystyle 120}(m-6)=5,\vspace{0.5em}\\
a_6=6+\frac{\displaystyle 5\cdot 4\cdot 3\cdot 2\cdot 1}{\displaystyle 120}(m-6)=6+(m-6)=m.