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EXAMPLE
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O.g.f.: A(x) = x + x^2 + 3*x^3 + 48*x^4 + 1125*x^5 + 74844*x^6 + 4538576*x^7 + 571979264*x^8 + 61768818081*x^9 + 11756208796500*x^10 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp(-n^3*A(x)) / (1 - n*x)^(n^2) begins:
n=1: [1, 0, -1, -16, -1143, -134816, -53867825, ...];
n=2: [1, 0, 0, -80, -8832, -1076928, -431006720, ...];
n=3: [1, 0, 27, 0, -24543, -3592512, -1464710445, ...];
n=4: [1, 0, 128, 896, 0, -7099904, -3495833600, ...];
n=5: [1, 0, 375, 4000, 371625, 0, -6020725625, ...];
n=6: [1, 0, 864, 11664, 2270592, 78335424, 0, ...];
n=7: [1, 0, 1715, 27440, 9134433, 444056032, 73395100555, 0, ...]; ...
in which the coefficient of x^n in row n forms a diagonal of zeros.
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