How to compute Binomial Coefficients in Nim (Useful as a kind of integer version of Gaussian distribution)

binomial.nim

import math

# See https://www.geeksforgeeks.org/space-and-time-efficient-binomial-coefficient/
# for details of this function
func binomialCoeff(n, k: int): int =
  var res = 1
  var k = k
  if (k > n - k):
    k = n - k
  for i in 0 ..< k:
    res = res * (n - i)
    res = res div (i + 1)
  return res

func binomialCoeffs(n: int): seq[int] =
  for i in 0 .. n:
    result.add(binomialCoeff(n, i))

func binomialNormCoeffs(n: int): seq[float32] =
  var arr = binomialCoeffs(n)
  let total = sum(arr).float32
  result = newSeq[float32](arr.len)
  for i, a in arr:
    result[i] = a.float32 / total

for n in 0 ..< 50:
  echo binomialNormCoeffs(n)