Question Number 185719 by Frix last updated on 26/Jan/23
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{next}\:\mathrm{number}: \\ $$$${a}_{\mathrm{0}} ={a}_{\mathrm{1}} =\mathrm{1},\:{a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{\mathrm{3}} =? \\ $$
Commented by Frix last updated on 26/Jan/23
...of course it's 42 ��
Commented by SEKRET last updated on 26/Jan/23
$$ \\ $$šš
Answered by Frix last updated on 26/Jan/23
$${a}_{{n}} =\frac{\left({n}^{\mathrm{2}} \right)!\underset{{k}=\mathrm{1}} {\overset{{n}ā\mathrm{1}} {\prod}}\:\frac{{k}!}{\left({n}+{k}\right)!}}{{n}!} \\ $$$${a}_{\mathrm{3}} =\mathrm{42} \\ $$