Pascal's triangle is a triangular array of Binomial coefficients. Review how Binomial coefficient is counted help. Lets implement this by using recursive relatioship of C(n, k), drived from Pascal's triangle, C(n, k) = C(n-1, k-1) + C(n-1, k), C(n, 0) = C(n, n) = 1.

# Python implementation

def binomial(n, k):
  if n < 0 or n < k:
    return 0

  if k == 0 or k == n:
    return 1

  return binomial(n - 1, k - 1) + binomial(n - 1, k)

n = 5
output = []

for i in range(n):
  result = []

  for j in range(i + 1):
    result.append(binomial(i, j))

  output.append(result)

print(output)

// Javascript implementation

function binomial(n, k) {
  if (n < 0 || n < k) {
    return 0;
  }

  if (k === 0 || k === n) {
    return 1;
  }

  return binomial(n - 1, k - 1) + binomial(n - 1, k);
}

const n = 5;
const output = [];

for(let i = 0; i < n; i++) {
  let result = [];

  for (let j = 0; j <= i; j++) {
    result.push(binomial(i, j));
  }

  output.push(result);
}

console.log(output);

Pascal's Triangle

Hint