Double-checked locking for growable array of binomial coefficients

Question

I'm trying to use double-checked locking to maintain an array of binomial coefficients, but I read recently that double-checked locking doesn't work. Efficiency is extremely important so using volatile isn't an option unless it's only inside the conditional statements. I can't see a way to use a static class with a singleton object (this is part of a framework and I don't know what kinds of numbers people will need to use the function for so I can't guess what the maximum chosen value will be or whether the function will be used at all). The only thing I can think of is to make everything not static and insist that each thread that needs to use this method instantiate a Choose object with its own array. It seems like that shouldn't be necessary.

public static final class Util{
/**
 * Static array of nCr values
 */
public static long[][] nCr_arr;

/**
 * Calculate binomial coefficient (n k)
 * 
 * @param n
 *            n
 * @param k
 *            k
 * @return n choose k
 */
public static long nCr(int n, int k) {
    if (k < 0)
        throw new ArithmeticException("Cannot choose a negative number");
    if (n < 0) {
        if (k % 2 == 0)
            return nCr(-n + k - 1, k);
        else
            return -nCr(-n + k - 1, k);
    }
    if (k > n)
        return 0;
    if (k > n / 2)
        k = n - k;
    if (nCr_arr == null) {
        synchronized (Util.class) {
            if (nCr_arr == null)
                nCr_arr = new long[n + 1][];
        }
    }
    if (nCr_arr.length <= n) {
        synchronized (Util.class) {
            if (nCr_arr.length <= n) {
                long[][] newNCR = new long[n + 1][];
                System.arraycopy(nCr_arr, 0, newNCR, 0, nCr_arr.length);
                nCr_arr = newNCR;
            }
        }
    }
    if (nCr_arr[n] == null) {
        synchronized (Util.class) {
            if (nCr_arr[n] == null)
                nCr_arr[n] = new long[k + 1];
        }
    }
    if (nCr_arr[n].length <= k) {
        synchronized (Util.class) {
            if (nCr_arr[n].length <= k) {
                long[] newNCR = new long[k + 1];
                System.arraycopy(nCr_arr[n], 0, newNCR, 0,
                        nCr_arr[n].length);
                nCr_arr[n] = newNCR;
            }
        }
    }
    if (nCr_arr[n][k] == 0) {
        if (k == 0)
            nCr_arr[n][k] = 1;
        else
            nCr_arr[n][k] = nCr(n, k - 1) * (n - (k - 1)) / k;
    }
    return nCr_arr[n][k];
}
}

Answer 1

I ended up just making it not static. If a thread needs to get nCr values, it creates a new Coefficient object and holds onto it.