An iterable stars and bars class in python

stars_bars.py

import math
import scipy.special as sci
class stars_bars:
    def __init__(self,nbins=4,nstars=40):
        self.nbins=nbins
        self.nstars=nstars
        self.bars=[0]*(nbins-1)  # bar positions; there are nbins-1 bars
        self.bins=[0]*nbins      # number of stars in each bin
        self.stars=[0]*nstars    # bin index of each star
        self.index=0             # arrangement counter
        self.narrangements=int(sci.comb(nstars+nbins-1,nbins-1)) # number of unique arrangements
        self.npermutations=0     # number of permutations of current arrangement (when iterating)
    def __iter__(self):
        self.index=-1
        # initially, all stars are in the right-most bin, and all bars at position-0
        for i in range(self.nbins-1):
            self.bars[i]=0
        self.bars[self.nbins-2]=-1
        for i in range(self.nbins):
            self.bins[i]=0
        for i in range(self.nstars):
            self.stars[i]=self.nbins-1
        self.bins[self.nbins-1]=self.nstars
        return self
    def compute_hist(self):
        stars = self.nstars
        for bar in range(self.nbins-2,-1,-1):
            stars2bin=stars-self.bars[bar]
            self.bins[bar+1]=stars2bin
            for star in range(stars-1,stars-stars2bin-1,-1):
                self.stars[star]=bar+1
            stars-=stars2bin
            if stars == 0:
                break
        self.bins[0]=stars
        # leftover stars 
        for star in range(stars-1,-1,-1):
            self.stars[star]=0
        self.npermutations=self.compute_npermut()
    def compute_npermut(self):
        den=1.0
        for b in self.bins:
            den*=math.factorial(b)
        return math.factorial(self.nstars)/den
    def slide_bar(self,i):
        if i>=0:
            self.bars[i]+=1
            if self.bars[i]==self.nstars+1:
                self.slide_bar(i-1)
                self.bars[i]=self.bars[i-1]
    def __next__(self):
        if self.bars[0]==self.nstars:
            raise StopIteration
        else:
            i=self.nbins-2
            self.slide_bar(i)
            self.compute_hist()
            self.index+=1
            return self
    def __str__(self):
        retval='{:7d}/{:<7d}: '.format(self.index,self.narrangements)
        if self.bars[0]!=0:
            retval+='*'*self.bins[0]
        for i in range(self.nbins-1):
            retval+='|'+'*'*self.bins[i+1]
        retval+=' ['
        for i in range(self.nbins):
            retval+='{:>2d}{}'.format(self.bins[i],',' if i<self.nbins-1 else '')
        retval+='] ('
        for i in range(self.nstars):
            retval+='{:d}{}'.format(self.stars[i],',' if i<self.nstars-1 else '')
        return retval+') '+'{:<20d}'.format(int(self.npermutations))
    def mean(self):
        tally=0
        denom=0
        for i in range(self.nbins):
            tally+=i*self.bins[i]
            denom+=self.bins[i]
        return round(tally/denom)
    
if __name__=='__main__':
    print('Stars and bars: an example')
    for s in stars_bars(nbins=4,nstars=10):
        print(s)