Maxima Function
multinomial_coeff (a_1, ..., a_n)
multinomial_coeff()
Returns the multinomial coefficient.
When each a_k is a nonnegative integer, the multinomial coefficient
gives the number of ways of placing a_1 + ... + a_n
distinct objects into n boxes with a_k elements in the
k'th box. In general, multinomial_coeff (a_1, ..., a_n)
evaluates to (a_1 + ... + a_n)!/(a_1! ... a_n!)
.
multinomial_coeff()
(with no arguments) evaluates to 1.
minfactorial
may be able to simplify the value returned by multinomial_coeff
.
Examples:
(%i1) multinomial_coeff (1, 2, x); (x + 3)! (%o1) -------- 2 x! (%i2) minfactorial (%); (x + 1) (x + 2) (x + 3) (%o2) ----------------------- 2 (%i3) multinomial_coeff (-6, 2); (- 4)! (%o3) -------- 2 (- 6)! (%i4) minfactorial (%); (%o4) 10