binomial -- binomial coefficient

• Usage:

  binomial(n,k)

• Inputs:
  • n, an integer or a ring element,
  • k, an integer, must be non-negative;
• Outputs:
  • a number, the binomial coefficient, the coefficient of $x^k$ in $(1+x)^n$ or $n(n-1)...(n-k+1)/k!$.

i1 : binomial(13,6)

o1 = 1716

i2 : binomial(-1,3)

o2 = -1

i3 : binomial(7.5, pi)

o3 = 46.76478688243245

o3 : RR (of precision 53)

i4 : R = QQ[x]

o4 = R

o4 : PolynomialRing

i5 : binomial(x + 3, 3)

     1 3    2   11
o5 = -x  + x  + --x + 1
     6           6

o5 : R