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A112107 G.f. A(x) satisfies A(A(A(x))) = B(x) (3rd self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3}, with B(0) = 0.

%I A112107 #10 Sep 07 2024 03:22:55
%S A112107 1,1,-1,3,-10,35,-119,360,-792,-33,12779,-82525,305861,-552011,
%T A112107 -126321,-8385020,138177591,-433073834,-5366414982,51203452090,
%U A112107 123835509276,-4174647911014,5274854624423,373574363131841,-2054088594386738,-34047892948849106,391005463740951942
%N A112107 G.f. A(x) satisfies A(A(A(x))) = B(x) (3rd self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3}, with B(0) = 0.
%e A112107 A(x) = x + x^2 - x^3 + 3*x^4 - 10*x^5 + 35*x^6 - 119*x^7 + ...
%e A112107 where A(A(A(x))) = x + 3*x^2 + 3*x^3 + 3*x^4 + 2*x^5 + ...
%e A112107 is the g.f. of A112106.
%o A112107 (PARI) {a(n,m=3)=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 A112107 Cf. A112106, A112104, A112105, A112108-A112127.
%K A112107 sign
%O A112107 1,4
%A A112107 _Paul D. Hanna_, Aug 27 2005