|
|
EXAMPLE
| G.f.: A(x)=1+x*B(x), B(x)=1+x*C(x)^2, C(x)=1+x*D(x)^3, D(x)=1+x*E(x)^4, ...
Also, the derivative of A(x) is the series:
A' = B+ x*C^2+ 2!*x^2*C*D^3+ 3!*x^3*C*D^2*E^4+ 4!*x^4*C*D^2*E^3*F^5+...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,1,2,7,36,245,2072,20913,245012,...]
B=[1,1,2,7,36,245,2072,20913,245012,3265581,...]
C=[1,1,3,15,103,888,9147,109150,1477575,22349316,...]
D=[1,1,4,26,224,2351,28760,399314,6183132,105455687,...]
E=[1,1,5,40,415,5145,73121,1162620,20358145,388334030,...]
F=[1,1,6,57,692,9906,160656,2884554,56502264,1195386975,...]
|
