The number of partitions of an integer into parts equal to , i.e. the number of solutions in non-negative integers of the equation
The generating function of the denumerants is
The simplest method of computing a denumerant is by Euler's recurrence relation:
Explicit formulas for certain denumerants may be obtained from the following theorem: If is the least common multiple of the numbers , then the denumerant
is a polynomial of degree with respect to .
|||J. Riordan, "An introduction to combinational analysis" , Wiley (1958)|
Denumerant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Denumerant&oldid=16405