Science and Education Publishing Turkish Journal of Analysis and Number Theory 2 4 2014 07 31 Generating Function for M(m,n) 125 129 EN Sabuj Das Haradhan Kumar Mohajan Premier University, Chittagong, Bangladesh TJANT2014244 10.12691/tjant-2-4-4 2014 04 04 2014 04 14 2014 07 31 This paper shows that the coefficient of x in the right hand side of the equation is an algebraic relation in terms of z. The exponent of z represents the crank of partitions of a positive integral value of n and also shows that the sum of weights of corresponding partitions of n is the sum of ordinary partitions of n and it is equal to the number of partitions of n with crank m. This paper shows how to prove the Theorem "The number of partitions of n with crank C()=m is M(m,n) for all n>1."