binomial

Function: binomial
Section: combinatorics
C-Name: binomial0
Prototype: GDG
Help: binomial(x,{k}): binomial coefficient x*(x-1)...*(x-k+1)/k! defined for
 k in Z and any x. If k is omitted and x an integer, return the vector
 [binomial(x,0),...,binomial(x,x)].
Doc: \idx{binomial coefficient} $\binom{x}{k}$.
 Here $k$ must be an integer, but $x$ can be any PARI object.
 \bprog
 ? binomial(4,2)
 %1 = 6
 ? n = 4; vector(n+1, k, binomial(n,k-1))
 %2 = [1, 4, 6, 4, 1]
 @eprog\noindent The argument $k$ may be omitted if $x = n$ is a
 nonnegative integer; in this case, return the vector with $n+1$
 components whose $k+1$-th entry is \kbd{binomial}$(n,k)$
 \bprog
 ? binomial(4)
 %3 = [1, 4, 6, 4, 1]
 @eprog