got stuck in recursive relation

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i was solving an expected value problem but i got stuck in finding recursive relation?

recursive equation is... $$ E[n-i]=1+\frac{i}{n}E[n-i-1]+\frac{n-i}{n}E[n-i+1] $$

  • $E[0]=0$
  • $E[1]=1$
  • $E[2]=4$

I know it a non homogeneous eqation so there will be perticular solution and general solution. i will appreciate if somebody help me out.