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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 14*x^2 + 192*x^3 + 6460*x^4 + 604352*x^5 +...
Let P(x) = 1/eta(x) denote the g.f. of the partition numbers A000041:
P(x) = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 +...
then a(n) is the coefficient of x^n in P(x)^(2^n):
P(x)^(2^0): [(1),1,2,3,5,7,11,15,22,30,42,56,77,101,135,176,...];
P(x)^(2^1): [1,(2),5,10,20,36,65,110,185,300,481,752,1165,...];
P(x)^(2^2): [1,4,(14),40,105,252,574,1240,2580,5180,10108,...];
P(x)^(2^3): [1,8,44,(192),726,2464,7704,22528,62337,164560,...];
P(x)^(2^4): [1,16,152,1088,(6460),33440,155584,663936,...];
P(x)^(2^5): [1,32,560,7040,70840,(604352),4528832,30529280,...];
P(x)^(2^6): [1,64,2144,49920,905840,13627264,(176638592),...]; ...
where terms in parenthesis form the initial terms of this sequence.
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