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EXAMPLE
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The product P(x,y) = Product_{n>=1} (1 - (x^n + y^n)) begins
P(x,y) = 1 + (-1*x - 1*y) + (-1*x^2 + 0*x*y - 1*y^2) + (0*x^3 + 1*x^2*y + 1*x*y^2 + 0*y^3) + (0*x^4 + 1*x^3*y + 0*x^2*y^2 + 1*x*y^3 + 0*y^4) + (1*x^5 + 1*x^4*y + 1*x^3*y^2 + 1*x^2*y^3 + 1*x*y^4 + 1*y^5) + (0*x^6 + 0*x^5*y + 0*x^4*y^2 - 2*x^3*y^3 + 0*x^2*y^4 + 0*x*y^5 + 0*y^6) + (1*x^7 + 0*x^6*y + 0*x^5*y^2 + 0*x^4*y^3 + 0*x^3*y^4 + 0*x^2*y^5 + 0*x*y^6 + 1*y^7) + (0*x^8 - 1*x^7*y + 0*x^6*y^2 - 1*x^5*y^3 - 2*x^4*y^4 - 1*x^3*y^5 + 0*x^2*y^6 - 1*x*y^7 + 0*y^8) + (0*x^9 - 1*x^8*y - 1*x^7*y^2 - 2*x^6*y^3 - 1*x^5*y^4 - 1*x^4*y^5 - 2*x^3*y^6 - 1*x^2*y^7 - 1*x*y^8 + 0*y^9) + (0*x^10 - 1*x^9*y + 0*x^8*y^2 + 0*x^7*y^3 + 1*x^6*y^4 - 2*x^5*y^5 + 1*x^4*y^6 + 0*x^3*y^7 + 0*x^2*y^8 - 1*x*y^9 + 0*y^10) + (0*x^11 - 1*x^10*y - 1*x^9*y^2 + 0*x^8*y^3 - 1*x^7*y^4 + 0*x^6*y^5 + 0*x^5*y^6 - 1*x^4*y^7 + 0*x^3*y^8 - 1*x^2*y^9 - 1*x*y^10 + 0*y^11) + (-1*x^12 - 1*x^11*y + 0*x^10*y^2 + 0*x^9*y^3 - 1*x^8*y^4 + 0*x^7*y^5 + 0*x^6*y^6 + 0*x^5*y^7 - 1*x^4*y^8 + 0*x^3*y^9 + 0*x^2*y^10 - 1*x*y^11 - 1*y^12) + (0*x^13 + 0*x^12*y - 1*x^11*y^2 + 1*x^10*y^3 + 1*x^9*y^4 + 1*x^8*y^5 + 1*x^7*y^6 + 1*x^6*y^7 + 1*x^5*y^8 + 1*x^4*y^9 + 1*x^3*y^10 - 1*x^2*y^11 + 0*x*y^12 + 0*y^13) + (0*x^14 + 0*x^13*y + 1*x^12*y^2 + 2*x^11*y^3 + 2*x^10*y^4 + 2*x^9*y^5 + 3*x^8*y^6 + 2*x^7*y^7 + 3*x^6*y^8 + 2*x^5*y^9 + 2*x^4*y^10 + 2*x^3*y^11 + 1*x^2*y^12 + 0*x*y^13 + 0*y^14) + (-1*x^15 + 0*x^14*y - 1*x^13*y^2 + 1*x^12*y^3 + 0*x^11*y^4 - 2*x^10*y^5 + 0*x^9*y^6 + 0*x^8*y^7 + 0*x^7*y^8 + 0*x^6*y^9 - 2*x^5*y^10 + 0*x^4*y^11 + 1*x^3*y^12 - 1*x^2*y^13 + 0*x*y^14 - 1*y^15) + ...
This square table of coefficients T(n,k) of x^n*y^k in P(x,y) begins
1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, ...;
-1, 0, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 1, ...;
-1, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 1, -1, 1, 0, ...;
0, 1, 1, -2, 0, -1, -2, 0, 0, 0, 1, 2, 1, 2, 1, 2, ...;
0, 1, 0, 0, -2, -1, 1, -1, -1, 1, 2, 0, 1, 1, 2, 0, ...;
1, 0, 0, -1, -1, -2, 0, 0, 1, 2, -2, 3, 2, 2, 0, -1, ...;
0, 0, 0, -2, 1, 0, 0, 1, 3, 0, 2, 0, -1, -1, -2, 1, ...;
1, -1, -1, 0, -1, 0, 1, 2, 0, 2, 1, 1, 0, -1, -3, 0, ...;
0, -1, 0, 0, -1, 1, 3, 0, 2, 1, 1, -1, -2, -1, -1, -3, ...;
0, -1, -1, 0, 1, 2, 0, 2, 1, 4, -2, -2, 0, -3, -3, -2, ...;
0, -1, 0, 1, 2, -2, 2, 1, 1, -2, -2, 0, -2, -2, -3, -4, ...;
0, -1, -1, 2, 0, 3, 0, 1, -1, -2, 0, 2, -5, -4, -2, -1, ...;
-1, 0, 1, 1, 1, 2, -1, 0, -2, 0, -2, -5, 0, -3, -2, 4, ...;
0, 0, -1, 2, 1, 2, -1, -1, -1, -3, -2, -4, -3, 4, 1, -5, ...;
0, 0, 1, 1, 2, 0, -2, -3, -1, -3, -3, -2, -2, 1, -2, 4, ...;
-1, 1, 0, 2, 0, -1, 1, 0, -3, -2, -4, -1, 4, -5, 4, 4, ...; ...
Alternatively, this sequence can be written as a triangle, starting as
1;
-1, -1;
-1, 0, -1;
0, 1, 1, 0;
0, 1, 0, 1, 0;
1, 1, 1, 1, 1, 1;
0, 0, 0, -2, 0, 0, 0;
1, 0, 0, 0, 0, 0, 0, 1;
0, -1, 0, -1, -2, -1, 0, -1, 0;
0, -1, -1, -2, -1, -1, -2, -1, -1, 0;
0, -1, 0, 0, 1, -2, 1, 0, 0, -1, 0;
0, -1, -1, 0, -1, 0, 0, -1, 0, -1, -1, 0;
-1, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, -1, -1;
0, 0, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 0, 0;
0, 0, 1, 2, 2, 2, 3, 2, 3, 2, 2, 2, 1, 0, 0;
-1, 0, -1, 1, 0, -2, 0, 0, 0, 0, -2, 0, 1, -1, 0, -1;
0, 1, 1, 2, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 1, 1, 0;
0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 0;
0, 1, 1, 2, 2, 2, -1, 1, 1, 4, 1, 1, -1, 2, 2, 2, 1, 1, 0;
0, 1, 0, 0, 0, 0, -1, 0, -1, -2, -2, -1, 0, -1, 0, 0, 0, 0, 1, 0;
0, 1, 1, 0, 0, -1, -2, -1, -2, -2, -2, -2, -2, -1, -2, -1, 0, 0, 1, 1, 0;
0, 1, 0, 0, 0, 1, 1, -3, -1, 0, 0, 0, 0, -1, -3, 1, 1, 0, 0, 0, 1, 0;
1, 1, 1, -1, 0, 1, -3, 0, -1, -3, -2, 2, -2, -3, -1, 0, -3, 1, 0, -1, 1, 1, 1;
0, 0, 0, -2, -1, -2, -3, -2, -3, -3, -2, -5, -5, -2, -3, -3, -2, -3, -2, -1, -2, 0, 0, 0;
0, 0, 0, -1, -1, -1, -4, -2, -5, -2, -3, -4, 0, -4, -3, -2, -5, -2, -4, -1, -1, -1, 0, 0, 0;
0, 0, 0, -3, -2, -3, -1, -2, -2, -3, -4, -2, -3, -3, -2, -4, -3, -2, -2, -1, -3, -2, -3, 0, 0, 0;
1, 0, 0, -2, -1, -1, -1, -1, -1, -3, 1, -1, -2, 4, -2, -1, 1, -3, -1, -1, -1, -1, -1, -2, 0, 0, 1; ...
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