The efficient recursive solution extracted from the BrickPileProblem.java (https://gist.github.com/marksto/ec0fb1d727f31b7b6db7cf7fed97f56e).

RecursiveBrickPileSolver.java

private static class RecursiveBrickPileSolver extends BrickPileSolver {

    // NOTE: The 'ConcurrentHashMap' implementation should be used instead
    //       in case this object is to be shared between multiple threads.
    final Map<Integer, double[]> cache = new HashMap<>();

    public RecursiveBrickPileSolver(double brickMass) {
        super(brickMass);
    }

    private double m(int row, int pos) {
        if (pos < 0 || pos > row) {
            return 0d;
        }
        return m;
    }

    private double W_m(int row, int pos) {
        return 0.5*(W(row, pos) + m(row, pos));
    }

    private double W_impl(int row, int pos) {
        if (pos < 0 || pos > row) {
            return 0d;
        }

        double[] cachedRow = cache.computeIfAbsent(
                row,
                key -> new double[row + 1]
        );
        double result = cachedRow[pos];
        if (result == 0d) {
            result = W_m(row, pos);
            cachedRow[pos] = result;
        }
        return result;
    }

    @Override
    public double W(int row, int pos) {
        return W_impl(row-1, pos-1) + W_impl(row-1, pos);
    }
}