0,4

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,...]

(PARI) a(n)=local(A); A=1+x+x*O(x^n); for(j=0, n-1, A=1+x*A^(n-j)); polcoeff(A, n)

Adjacent sequences: A095790 A095791 A095792 this_sequence A095794 A095795 A095796

Sequence in context: A119736 A088715 A088313 this_sequence A029768 A007889 A125033

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 06 2004