fun.cs

void Main()
{
    Make.Fix<int>(f => n => n < 2 ? 1 : f(n - 1) * n)(5).Dump(); // 120
}

public class Make
{
    public static Func<T, T> Fix<T>(Func<Func<T, T>, Func<T, T>> func) { return Fun<T>.Fix(func); }
    public static Func<T, T> Fix<T>(Func<Func<T, T>, Func<T, T>> func, T dummy) { return Fun<T>.Fix(func); }
    private static class Fun<T>
    {
        private delegate U SelfApplicable<U>(SelfApplicable<U> self);
        private static SelfApplicable<Func<Func<Func<T, T>, Func<T, T>>, Func<T, T>>> Y = y => f => x => f(y(y)(f))(x);
        public static Func<Func<Func<T, T>, Func<T, T>>, Func<T, T>> Fix = Y(Y);
    }
}