`Base.binomial` returns `Float64` for `Integer` inputs of different types.

[sgaure]

The docs say

binomial(n::Integer, k::Integer)

  The binomial coefficient \binom{n}{k}, being the coefficient of the kth term in the polynomial
  expansion of (1+x)^n.

which isn't strictly true. When n and k have different integer types, the generalized binomial coefficient is returned, i.e. from binomial(x::Number, k::Integer).

julia> binomial(4, 2)
6

julia> binomial(Int32(4), 2)
6.0

julia> binomial(Int32(4), Int32(2))
6

[barucden]

Add

binomial(n::Integer, k::Integer) = binomial(promote(n, k)...)

? Then

julia> binomial(Int32(4), Int64(2)) 
6 # typeof(6) == Int64

[jishnub]

A PR is welcome