Declaring a density function with for loop

I have an extended binomial distribution which has the following form: 

 http://r.789695.n4.nabble.com/file/n4635699/kb.png 

Here alpha and beta are two parameters and x=0,1,2,3,...n (alike the
binomial distribution) 
I am writing a function to find out the densities (probabilities) of this
distribution for given values of alpha and beta. The below is the my
function... 

dnewdis<-function(x,a,b,n) { 
      term<-0 
      for (j in 0:exp(10)) { 
           term=term+(((-1)**i)*(choose(b-1,i))*(beta(x+a+a*i,n-x+1))) 
           } 
      s=a*b*choose(n,x)*term 
      return(s) 
      }