|
%I #19 Mar 30 2012 18:37:28
%S 1,1,-2,6,-30,184,-1294,10034,-83908,746006,-6983600,68360302,
%T -696122684,7345561204,-80074813040,899590031932,-10394864935860,
%U 123344285904634,-1500938535372826,18709376854618500,-238664936823622052,3113060999816038350
%N G.f. A(x) satisfies: A(A(x)) = (1+x-x^2)*A(x).
%F The series reversion of A(x) is -G(-x) where G(x) is the g.f. of A195440, which satisfies: G(x - x*G(x) - x*G(x)^2) = x.
%e G.f.: A(x) = x + x^2 - 2*x^3 + 6*x^4 - 30*x^5 + 184*x^6 - 1294*x^7 +...
%e where A(A(x)) = (1+x-x^2)*A(x) begins:
%e A(A(x)) = x + 2*x^2 - 2*x^3 + 3*x^4 - 22*x^5 + 148*x^6 - 1080*x^7 +...
%e The series reversion of A(x) begins:
%e -G(-x) = x - x^2 + 4*x^3 - 21*x^4 + 134*x^5 - 968*x^6 + 7662*x^7 +...
%e where G(x) is the g.f. of A195440.
%o (PARI) {a(n)=local(A, B, F); if(n<1, 0, F=x+x^2+x*O(x^n); A=F;
%o for(j=0, n, for(i=0, j, B=serreverse(A); A=(A+subst(B, x, A*(1+x-x^2) ))/2); A=round(A)); polcoeff(A, n, x))}
%Y Cf. A195440, A107095.
%K sign
%O 1,3
%A _Paul D. Hanna_, Sep 23 2011
|
