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EXAMPLE
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Row g.f.s R_n(y) simultaneously satisfy:
R_n(y) = 1 + y*R_1(y)^n + y^2*R_2(y)^(2n) + y^3*R_3(y)^(3n) +...
more explicitly:
R_0 = 1 + y + y^2 + y^3 + y^4 + ...
R_1 = 1 + y*(R_1)^1 + y^2*(R_2)^2 + y^3*(R_3)^3 + y^4*(R_4)^4 + ...
R_2 = 1 + y*(R_1)^2 + y^2*(R_2)^4 + y^3*(R_3)^6 + y^4*(R_4)^8 +...
R_3 = 1 + y*(R_1)^3 + y^2*(R_2)^6 + y^3*(R_3)^9 + y^4*(R_4)^12 +...
R_4 = 1 + y*(R_1)^4 + y^2*(R_2)^8 + y^3*(R_3)^12 + y^4*(R_4)^16 +...
etc., for all rows.
Rectangular table begins:
1,1,1,1,1,1,1,1,1,1,1,1,1,...
1,1,2,5,16,62,274,1332,6978,38873,228090,1399625,8933506,...
1,1,3,10,39,174,858,4564,25793,153301,951325,6130757,40861658,...
1,1,4,16,71,351,1891,10888,66139,420235,2775981,18978873,...
1,1,5,23,113,608,3535,21844,141809,959882,6738850,48877221,...
1,1,6,31,166,961,5977,39363,271564,1949165,14487241,111115804,...
1,1,7,40,231,1427,9430,65810,480077,3637345,28502254,230271472,...
1,1,8,50,309,2024,14134,104028,798954,6363948,52370770,443997440,...
1,1,9,61,401,2771,20357,157383,1267833,10579140,91111871,...
1,1,10,73,508,3688,28396,229810,1935562,16866694,151563677,...
1,1,11,86,631,4796,38578,325860,2861457,25969694,242836861,...
1,1,12,100,771,6117,51261,450748,4116641,38819122,376841378,...
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