A141382 - OEIS

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

%S 1,1,6,58,702,9830,152632,2565042,45938878,867667140,17154629472,

%T 353091007048,7534733877540,166160874412976,3777158124019664,

%U 88326122515058436,2121170864722835600,52242518805270485716

%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 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...

%e Related expansions:

%e A(A(x)) = x + 2*x^2 + 14*x^3 + 147*x^4 + 1890*x^5 + 27732*x^6 +...

%e A(A(A(x))) = x + 3*x^2 + 24*x^3 + 273*x^4 + 3730*x^5 + 57488*x^6 +...

%e A(A(A(A(x)))) = x + 4*x^2 + 36*x^3 + 442*x^4 + 6412*x^5 + 103890*x^6 +...

%e A(A(A(A(x)))^2) = x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...

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

%e A(A(A(x))^2) = x^2 + 4*x^3 + 33*x^4 + 358*x^5 + 4650*x^6 + 68168*x^7 +...

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

%Y Cf. A141380, A141381, A141383; A141371.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jun 28 2008