Programming Forums - Multi-dimensional vectors

I'm creating a program to help me solve polynomial multiplication so I won't have to do all that multiplying.(I'm lazy. :P)And I have run into a problem. I found that in order for the multiplication to turn out right I have to create dynamic two-dimensional arrays. I messed with new for a bit until I just figured it would be more efficient to just use the vector class. But the problem is I keep on getting "Vector subscript out of range" when I get to a certain point in my program(commented bellow).

// main.cpp -- This program will solve any number of binomials multiplied together
#include <iostream>
#include <vector>
using std::vector;
using std::cout;
using std::cin;
using std::endl;
 
int main()
{
        char again = 'y';
 
        cout << "Programed by Shawn Stovall(With assistance from Carl Bondy)\n04-10-08\nPROTOTYPE\n\n";
 
        while(again != 'n')
        {
                vector<double> coeff;
                vector<double> lone;
                vector<vector<double> > coeff_sqr;
                vector<vector<double> > coeff_ans;
                vector<vector<double> > coeff_ans2;
                vector<vector<double> > lone_ans;
                int num_poly;
 
                cout << "Please enter the number of binomials in your problem: ";
                cin >> num_poly;
 
                coeff.resize(num_poly);
                lone.resize(num_poly);
                coeff_sqr.resize(num_poly);
                coeff_ans.resize(num_poly);
                coeff_ans2.resize(num_poly);
                lone_ans.resize(num_poly);
 
                for(int i = 0; i < num_poly; i++)
                {
                        coeff_sqr[i].resize(num_poly);
                        coeff_ans[i].resize(num_poly);
                        coeff_ans2[i].resize(num_poly);
                        lone_ans[i].resize(num_poly);
                }
 
                cout << "Each binomial will be in the form: \n\n([coefficient]x + [number])"
                            "\nExample: (x + 7)(5x + -3)\n\n"
                                "Please enter the binomials:\n";
 
                for(int i = 0; i < num_poly; i++)
                {
                        cout << "\nBinomial #" << i + 1 << endl;
                        cout << "Coefficient: ";
                        cin >> coeff[i];
                        cout << "Number: ";
                        cin >> lone[i];
                        cout << endl;
                }
 
                for(int i = 0; i < (num_poly - 1); i++)                    // This loop
                        for(int j = 1; j >= (num_poly - 1); j += 2)
                        {
                                int t = 1;
                                coeff_sqr[i].at(j - t) = coeff[i] * coeff[j];
                                coeff_ans[i].at(j - t) = coeff[i] * lone[j];
                                coeff_ans2[i].at(j - t) = lone[i] * coeff[j];
                                lone_ans[i].at(j - t) = lone[i] * lone[j];
                                t++;
                        }
 
                double fin_coeff_sqr = 0;
 
                for(int i = 0; i < (num_poly - 1); i++)
                {
                        double temp = coeff_sqr[i][0];
 
                        for(int j = 1; j < (num_poly - 1); j++)
                                temp += coeff_sqr[i][j];
 
                        fin_coeff_sqr += temp;
                }
 
                double fin_coeff_ans = 0;
 
                for(int i = 0; i < (num_poly - 1); i++)
                {
                        double temp = coeff_ans[i][0] + coeff_ans[i][0];
 
                        for(int j = 1; j < (num_poly - 1); j++)
                                temp += coeff_ans[i][j] + coeff_ans2[i][j];
 
                        fin_coeff_ans += temp;
                }
 
                double fin_lone = 0;
 
                for(int i = 0; i < (num_poly - 1); i += 2)
                {
                        double temp = lone_ans[i][0];
 
                        for(int j = 1; j < (num_poly - 1); j++)
                                temp += lone_ans[i][j];
 
                        fin_lone += temp;
                }
 
                cout << "\nThe answer is " << fin_coeff_sqr << "x^2+" << fin_coeff_ans << "x+" << fin_lone << endl;
                cout << "\nWould you like to go again? (y/n) ";
                cin >> again;
        }
 
        cout << "\nGoodbye!\n\n";
        return 0;
}

Any pointers or help would be highly appreciated! Thanks.

int t = 1;
for(int i = 0; i < (num_poly - 1); i++)
for(int j = 1; j >= (num_poly - 1); j += 2)
{
coeff_sqr[i].at(j - t) = coeff[i] * coeff[j];
coeff_ans[i].at(j - t) = coeff[i] * lone[j];
coeff_ans2[i].at(j - t) = lone[i] * coeff[j];
lone_ans[i].at(j - t) = lone[i] * lone[j];
t++;
}