Find-the-next-number-a-0-a-1-1-a-2-2-a-3-

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

$$ \\ $$😁😁

Answered by Frix last updated on 26/Jan/23

$${a}_{{n}} =\frac{\left({n}^{\mathrm{2}} \right)!\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\:\frac{{k}!}{\left({n}+{k}\right)!}}{{n}!} \\ $$$${a}_{\mathrm{3}} =\mathrm{42} \\ $$

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