Task: Pascal matrix generation
C#: using System;

public static class PascalMatrixGeneration
{
    public static void Main() {
        Print(GenerateUpper(5));
        Console.WriteLine();
        Print(GenerateLower(5));
        Console.WriteLine();
        Print(GenerateSymmetric(5));
    }

    static int[,] GenerateUpper(int size) {
        int[,] m = new int[size, size];
        for (int c = 0; c < size; c++) m[0, c] = 1;
        for (int r = 1; r < size; r++) {
            for (int c = r; c < size; c++) {
                m[r, c] = m[r-1, c-1] + m[r, c-1];
            }
        }
        return m;
    }

    static int[,] GenerateLower(int size) {
        int[,] m = new int[size, size];
        for (int r = 0; r < size; r++) m[r, 0] = 1;
        for (int c = 1; c < size; c++) {
            for (int r = c; r < size; r++) {
                m[r, c] = m[r-1, c-1] + m[r-1, c];
            }
        }
        return m;
    }

    static int[,] GenerateSymmetric(int size) {
        int[,] m = new int[size, size];
        for (int i = 0; i < size; i++) m[0, i] = m[i, 0] = 1;
        for (int r = 1; r < size; r++) {
            for (int c = 1; c < size; c++) {
                m[r, c] = m[r-1, c] + m[r, c-1];
            }
        }
        return m;
    }

    static void Print(int[,] matrix) {
        string[,] m = ToString(matrix);
        int width = m.Cast<string>().Select(s => s.Length).Max();
        int rows = matrix.GetLength(0), columns = matrix.GetLength(1);
        for (int row = 0; row < rows; row++) {
            Console.WriteLine("|" + string.Join(" ", Range(0, columns).Select(column => m[row, column].PadLeft(width, ' '))) + "|");
        }
    }

    static string[,] ToString(int[,] matrix) {
        int rows = matrix.GetLength(0), columns = matrix.GetLength(1);
        string[,] m = new string[rows, columns];
        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < columns; c++) {
                m[r, c] = matrix[r, c].ToString();
            }
        }
        return m;
    }
    
}

Java: import static java.lang.System.out;
import java.util.List;
import java.util.function.Function;
import java.util.stream.*;
import static java.util.stream.Collectors.toList;
import static java.util.stream.IntStream.range;

public class PascalMatrix {
    static int binomialCoef(int n, int k) {
        int result = 1;
        for (int i = 1; i <= k; i++)
            result = result * (n - i + 1) / i;
        return result;
    }

    static List<IntStream> pascal(int n, Function<Integer, IntStream> f) {
        return range(0, n).mapToObj(i -> f.apply(i)).collect(toList());
    }

    static List<IntStream> pascalUpp(int n) {
        return pascal(n, i -> range(0, n).map(j -> binomialCoef(j, i)));
    }

    static List<IntStream> pascalLow(int n) {
        return pascal(n, i -> range(0, n).map(j -> binomialCoef(i, j)));
    }

    static List<IntStream> pascalSym(int n) {
        return pascal(n, i -> range(0, n).map(j -> binomialCoef(i + j, i)));
    }

    static void print(String label, List<IntStream> result) {
        out.println("\n" + label);
        for (IntStream row : result) {
            row.forEach(i -> out.printf("%2d ", i));
            System.out.println();
        }
    }

    public static void main(String[] a) {
        print("Upper: ", pascalUpp(5));
        print("Lower: ", pascalLow(5));
        print("Symmetric:", pascalSym(5));
    }
}