Question Number 30750 by abdo imad last updated on 25/Feb/18
$${f}\:{function}\:{C}^{\infty} \:/{f}^{'} =\mathrm{1}+{f}^{\mathrm{2}} \:\:{let}\:{take}\:{a}_{{k}} =\frac{{f}^{\left({k}\right)} \left(\mathrm{0}\right)}{{k}!}\: \\ $$$${prove}\:{that}\:{a}_{{n}+\mathrm{1}} =\:\frac{\mathrm{1}}{{n}+\mathrm{1}}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{a}_{{k}} \:\:{a}_{{n}−{k}} \\ $$