G.f.: B(x) = (1/x) * Series_Reversion( x*(1 - 2*x)^3 / ((1 - x^2)*(1 + 2*x)) ).
G.f. B = B(x) and related functions A = A(x), C = C(x), D = D(x), E = E(x), satisfy:
(1.a) A = 1/((1 - 2*x*B)*(1 - 3*x*C)*(1 - 4*x*D)).
(1.b) B = 1/((1 - x*A)*(1 - 3*x*C)*(1 - 4*x*D)).
(1.c) C = 1/((1 - x*A)*(1 - 2*x*B)*(1 - 4*x*D)).
(1.d) D = 1/((1 - x*A)*(1 - 2*x*B)*(1 - 3*x*C)).
(1.e) E = 1/((1 - x*A)*(1 - 2*x*B)*(1 - 3*x*C)*(1 - 4*x*D)).
(1.f) E = (A*B*C*D)^(1/3).
(2.a) A = (1 + 2*x*E)*(1 + 3*x*E)*(1 + 4*x*E).
(2.b) B = (1 + x*E)*(1 + 3*x*E)*(1 + 4*x*E).
(2.c) C = (1 + x*E)*(1 + 2*x*E)*(1 + 4*x*E).
(2.d) D = (1 + x*E)*(1 + 2*x*E)*(1 + 3*x*E).
(2.e) E = (1 + x*E)*(1 + 2*x*E)*(1 + 3*x*E)*(1 + 4*x*E).
(3.a) A = B/(1 - x*B) = C/(1 - 2*x*C) = D/(1 - 3*x*D) = E/(1 + x*E).
(3.b) B = A/(1 + x*A) = C/(1 - x*C) = D/(1 - 2*x*D) = E/(1 + 2*x*E).
(3.c) C = A/(1 + 2*x*A) = B/(1 + x*B) = D/(1 - x*D) = E/(1 + 3*x*E).
(3.d) D = A/(1 + 3*x*A) = B/(1 + 2*x*B) = C/(1 + x*C) = E/(1 + 4*x*E).
(3.e) E = A/(1 - x*A) = B/(1 - 2*x*B) = C/(1 - 3*x*C) = D/(1 - 4*x*D).
(3.f) 1 = (1 + x*A)*(1 - x*B) = (1 + 2*x*A)*(1 - 2*x*C) = (1 + 3*x*A)*(1 - 3*x*D) = (1 + x*B)*(1 - x*C) = (1 + 2*x*B)*(1 - 2*x*D) = (1 + x*C)*(1 - x*D).
(3.g) 1 = (1 - x*A)*(1 + x*E) = (1 - 2*x*B)*(1 + 2*x*E) = (1 - 3*x*C)*(1 + 3*x*E) = (1 - 4*x*D)*(1 + 4*x*E).
(4.a) A = (1 + x*A)*(1 + 2*x*A)*(1 + 3*x*A)/(1 - x*A)^3.
(4.b) B = (1 - x^2*B^2)*(1 + 2*x*B)/(1 - 2*x*B)^3.
(4.c) C = (1 - x^2*C^2)*(1 - 2*x*C)/(1 - 3*x*C)^3.
(4.d) D = (1 - x*D)*(1 - 2*x*D)*(1 - 3*x*D)/(1 - 4*x*D)^3.
(4.e) E = (1 + x*E)*(1 + 2*x*E)*(1 + 3*x*E)*(1 + 4*x*E).
(5.a) A = (1/x)*Series_Reversion( x*(1 - x)^3 / ((1 + x)*(1 + 2*x)*(1 + 3*x)) ).
(5.b) B = (1/x)*Series_Reversion( x*(1 - 2*x)^3 / ((1 - x^2)*(1 + 2*x)) ).
(5.c) C = (1/x)*Series_Reversion( x*(1 - 3*x)^3 / ((1 - x^2)*(1 - 2*x)) ).
(5.d) D = (1/x)*Series_Reversion( x*(1 - 4*x)^3 / ((1 - x)*(1 - 2*x)*(1 - 3*x)) ).
(5.e) E = (1/x)*Series_Reversion( x / ((1 + x)*(1 + 2*x)*(1 + 3*x)*(1 + 4*x)) ).
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