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EXAMPLE
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O.g.f.: A(x) = 1 + x - 3*x^3 - 5*x^4 + 10*x^5 + 58*x^6 + 23*x^7 - 557*x^8 - 1421*x^9 + 4094*x^10 + 28316*x^11 - 52*x^12 - 449150*x^13 - 970286*x^14 + ...
ILLUSTRATION OF DEFINITION.
The table of coefficients of x^k/k! in exp( n*x*A(x) ) * (n+1 - n*A(x)) begins:
n=1: [1, 0, 1, 16, 117, -704, -35075, -200304, 17660041, ...];
n=2: [1, 0, 0, 20, 288, 912, -51200, -888480, 19165440, ...];
n=3: [1, 0, -3, 0, 333, 3888, -27135, -1471824, 4665465, ...];
n=4: [1, 0, -8, -56, 0, 5344, 33280, -1317312, -15647744, ...];
n=5: [1, 0, -15, -160, -1035, 0, 81325, -180000, -25008375, ...];
n=6: [1, 0, -24, -324, -3168, -20304, 0, 1156896, -10209024, ...];
n=7: [1, 0, -35, -560, -6867, -67088, -422975, 0, 19205305, ...];
n=8: [1, 0, -48, -880, -12672, -155712, -1525760, -9408384, 0, ...];
n=9: [1, 0, -63, -1296, -21195, -305856, -3806595, -37346832, -230393079, 0, ...]; ...
in which the coefficients of x^n in row n form a diagonal of zeros.
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