title: Sum Binomial Coefficients
signature: function sumBinomialCoefficients($n) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($n, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($n), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        8, 
        256));
      
      printf("TEST-1...%s\n",driver(
        39, 
        549755813888));
      
      printf("TEST-2...%s\n",driver(
        25, 
        33554432));
      
      printf("TEST-3...%s\n",driver(
        44, 
        17592186044416));
      
      printf("TEST-4...%s\n",driver(
        6, 
        64));
      
      printf("TEST-5...%s\n",driver(
        48, 
        281474976710656));
      
      printf("TEST-6...%s\n",driver(
        39, 
        549755813888));
      
  }
  
  main();
  ?>
source_py: def sum_binomial_coefficients(n):
      C = [([0] * (n + 2)) for i in range(0, (n + 2))]
      for i in range(0, (n + 1)):
          for j in range(0, (min(i, n) + 1)):
              if ((j == 0) or (j == i)):
                  C[i][j] = 1
              else:
                  C[i][j] = (C[(i - 1)][(j - 1)] + C[(i - 1)][j])
      sum = 0
      for i in range(0, (n + 1)):
          sum += C[n][i]
      return sum
source_cpp: int sum_binomial_coefficients(int n) {
    int C [ n + 1 ] [ n + 1 ];
    for ( int i = 0;
    i <= n;
    i ++ ) {
      for ( int j = 0;
      j <= min ( i, n );
      j ++ ) {
        if ( j == 0 || j == i ) C [ i ] [ j ] = 1;
        else C [ i ] [ j ] = C [ i - 1 ] [ j - 1 ] + C [ i - 1 ] [ j ];
      }
    }
    int sum = 0;
    for ( int i = 0;
    i <= n;
    i ++ ) sum += C [ n ] [ i ];
    return sum;
  }