The number of multinomial coefficients based on a set of partitions of n   into k parts and divided by k evenly
  In this paper we obtained an original integer sequence based on the properties of the multinomial coefficient. We investigated a property of the sequence that shows connection with a primality testing. For any prime n the n-th term in the sequence is less by 1 than the number of partitions of n. We hypothesize the existence of an asymptotic algorithm of primality testing. 
Dmitry Kruchinin
math.CO math.NT