Question Number 561 by 123456 last updated on 27/Jan/15
$${a}_{{n}+\mathrm{2}} =\frac{{a}_{{n}+\mathrm{1}} +{a}_{{n}} +{a}_{{n}+\mathrm{1}} {a}_{{n}} }{\mathrm{3}},{a}_{\mathrm{0}} ={e},{a}_{\mathrm{1}} =\pi \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} =? \\ $$