%I #6 Mar 14 2015 10:04:25

%S 1,1,-2,8,-38,194,-992,4777,-19831,56116,48008,-2062286,16053636,

%T -70193968,155216743,-968038798,23817048561,-233579083166,333773365,

%U 21684104628935,-121906541882294,-2171063003748135,30425707365005935,192144123118329872

%N G.f. A(x) satisfies A(A(A(A(x)))) = B(x) (4th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,4}, with B(0) = 0.

%e A(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 +...

%e where A(A(A(A(x)))) =

%e x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + 4*x^7 + 4*x^8 +...

%e is the g.f. of A112108.

%o (PARI) {a(n,m=4)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); return(polcoeff(F,n,x)))}

%Y Cf. A112108, A112104-A112107, A112110-A112127.

%K sign

%O 1,3

%A _Paul D. Hanna_, Aug 27 2005