Navigation

Operators and Keywords

Function List:

C++ API

Function File: [c alpha] = multinom_coeff (m, n)

Function File: [c alpha] = multinom_coeff (m, n,order)

Produces the coefficients of the multinomial expansion 

          (x1 + x2 + ... + xm).^n

For example, for m=3, n=3 the expansion is 

          (x1+x2+x3)^3 =
                  = x1^3 + x2^3 + x3^3 +
                  +  3 x1^2 x2 + 3 x1^2 x3 + 3 x2^2 x1 + 3 x2^2 x3 +
                  + 3 x3^2 x1 + 3 x3^2 x2 + 6 x1 x2 x3

and the coefficients are [6 3 3 3 3 3 3 1 1 1].

The order of the coefficients is defined by the optinal argument order. It is passed to the function multion_exp. See the help of that function for explanation. The multinomial coefficients are generated using 

           /   \
           | n |                n!
           |   |  = ------------------------
           | k |     k(1)!k(2)! ... k(end)!
           \   /

See also: multinom multinom_exp

Demonstration 1

The following code

 multinom_coeff(3,3)
 multinom_coeff(3,3,'ascend')
 multinom_coeff(3,3,'descend')

Produces the following output

ans =

   1
   3
   3
   3
   6
   3
   1
   3
   3
   1

ans =

   6
   3
   3
   3
   3
   3
   3
   1
   1
   1

ans =

   1
   1
   1
   3
   3
   3
   3
   3
   3
   6

Package: specfun