Let a1=0 and a2=1.
an=n2an-1+n2(n-1)an-2+(-1)n(1-n2).
Find f=an+2 nC2an-1 +3 nC3an-2+...+na1.
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3 Answers
39this has got quite a bit of working..
no hands prophet sir or nishant bhaiyan ?
341nope, another chinese MO problem and i will end up on a psychiatrist's couch.
If you can give the solution, I will be very pleased
111stly, if I'm not wrong, the qsn needs slight modification..
The last term is not na1, but n2a1.
If u need the function it is 2.n!-n-1.
Do not ask me to derive it. I saw the soln in a book by Andreescu, Feng & Lee, where they used induction to prove that an is the number of derangements of the set of the 1st n naturals.....
I can however copy-paste it if anyone desires to have a look.......