The special multinomial distribution we shall define deals with n identical objects subdivided into m non-empty non-distinct sets.Take the particular example, in which we have n identical quanta of energy to be shared by m identical molecules.We shall let Dnm denote the number of distinct distributions in which we have n identical quanta shared among exactly m, no more and no less, identical molecules.The number Dnm is called the distribution number or briefly as the D-number.