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A112109 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.

%I A112109 #6 Mar 14 2015 10:04:25
%S A112109 1,1,-2,8,-38,194,-992,4777,-19831,56116,48008,-2062286,16053636,
%T A112109 -70193968,155216743,-968038798,23817048561,-233579083166,333773365,
%U A112109 21684104628935,-121906541882294,-2171063003748135,30425707365005935,192144123118329872
%N A112109 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 A112109 A(x) = x + x^2 - 2*x^3 + 8*x^4 - 38*x^5 + 194*x^6 - 992*x^7 +...
%e A112109 where A(A(A(A(x)))) =
%e A112109 x + 4*x^2 + 4*x^3 + 2*x^4 + 4*x^5 + 2*x^6 + 4*x^7 + 4*x^8 +...
%e A112109 is the g.f. of A112108.
%o A112109 (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 A112109 Cf. A112108, A112104-A112107, A112110-A112127.
%K A112109 sign
%O A112109 1,3
%A A112109 _Paul D. Hanna_, Aug 27 2005