whats the logic behind calculating f(n)=1n∗2n−1∗3n−2∗…∗n1

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if it is related to the last day contest, then it is superfactorial concept!!

you can search about it on the internet

We know f(1) = 1, f(2) = 1x1x2

Consider f(3) , f(4), f(5) values.

f(3)=1x1x1x2x2x3 which is nothing but

f(3)=(1x2x3) x(1x1x2) when rewritten, similarily

f(4)=1x1x1x1x2x2x2x3x3x4 when rewritten,

f(4)=(1x2x3x4) x(1x1x1x2x2x3) =(1x2x3x4) x((1x2x3)x(1x1x2))

f(5) =1x1x1x1x1x2x2x2x2x3x3x3x4x4x5

When rewritten just like f(4) we get

f(5)=(1x2x3x4x5) x((1x2x3x4)x((1x2x3)x(1x1x2)))

Now, on observing those values, we get

f(n) = n! x f(n-1)

Thats it

Hope it helps.

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For any ‘i’, answer is:-

f(i) = f(i-1)*(1*2*3*4.....*i)

Pre-compute these values and you are done.

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The Function simply imlies:

f(n)=n!*f(n-1)

that’s it

thank you

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