(binomial=
  n k coef
.   !arg:(?n,?k)
  & (!n+-1*!k:<!k:?k|)
  & 1:?coef
  &   whl
    ' ( !k:>0
      & !coef*!n*!k^-1:?coef
      & !k+-1:?k
      & !n+-1:?n
      )
  & !coef
);

binomial$(5,3)
10