[tex]a_n=(n+1)\cdot(2n+3)=2n^2+3n+2n+3=2n^2+5n+3[/tex]
[tex]a_0=2\cdot0^2+5\cdot0+3=3[/tex]
[tex]a_{n+1}=(n+1+1)\cdot(2\cdot(n+1)+3)=(n+2)\cdot(2n+2+3)=(n+2)\cdot(2n+5)=\\\\2n^2+5n+4n+10=2n^2+5n+3+4n+7=a_n+4n+7[/tex]
[tex]\begin{cases}a_0=3\\a_{n+1}=a_n+4n+7 \end{cases} [/tex]
