A141383 - OEIS

%I #2 Mar 30 2012 18:37:10

%S 1,1,8,104,1724,33280,715308,16683724,415466708,10926375108,

%T 301131874516,8648002744564,257687247253732,7940507243098200,

%U 252374158974639744,8255994209084399972,277508512417717367138

%N G.f. satisfies: A(x) = x + A(A(A(A(x))))^2.

%F G.f. satisfies: A( x - A(A(A(x)))^2 ) = x.

%e G.f.: A(x) = x + x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...

%e Related expansions:

%e A(A(x)) = x + 2*x^2 + 18*x^3 + 249*x^4 + 4304*x^5 + 85740*x^6 +...

%e A(A(A(x))) = x + 3*x^2 + 30*x^3 + 441*x^4 + 7958*x^5 + 163940*x^6 +...

%e A(A(A(A(x)))) = x + 4*x^2 + 44*x^3 + 686*x^4 + 12928*x^5 + 275758*x^6 +...

%e A(A(A(A(x))))^2 = x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...

%e The series reversion of A(x) = x - A(A(A(x)))^2, where

%e A(A(A(x)))^2 = x^2 + 6*x^3 + 69*x^4 + 1062*x^5 + 19462*x^6 + 402088*x^7 +...

%o (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=x+subst(A^2,x,subst(A,x,subst(A,x,A+x*O(x^n)))));polcoeff(A,n)}

%Y Cf. A141380, A141381, A141382; A141372.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jun 28 2008