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%I #7 Aug 03 2012 14:49:31
%S 1,1,1,19,163,2269,34093,584767,10989271,224143489,4910384809,
%T 114714875755,2841991084747,74337591206629,2045557726962949,
%U 59036247882081847,1782385894711138303,56166016733387381449,1843556640469175481985,62915735570546535121891
%N G.f. A(x) satisfies: A(A(A(x))) = G(x) where G(x) = x + 2*x^2 + x*G(G(G(x))) is the g.f. of A215114.
%F a(n) == 1 (mod 18).
%e G.f.: A(x) = x + x^2 + x^3 + 19*x^4 + 163*x^5 + 2269*x^6 + 34093*x^7 +...
%e Let G(x) = A(A(A(x))):
%e G(x) = x + 3*x^2 + 9*x^3 + 81*x^4 + 891*x^5 + 11907*x^6 + 184437*x^7 +...
%e such that G(x) = x + 2*x^2 + x*G(G(G(x))):
%e G(G(G(x))) = x + 9*x^2 + 81*x^3 + 891*x^4 + 11907*x^5 + 184437*x^6 +...
%o (PARI) {a(n)=local(A=x+x^2, B=x+2*x^2); for(i=1, n+1, B=x+2*x^2+x*subst(B, x, subst(B, x, B+x*O(x^n))));
%o for(j=1, n+1, A=round((2*A+subst(B, x, serreverse(subst(A,x,A+x*O(x^n)))))/3));; polcoeff(A, n)}
%o for(n=1, 31, print1(a(n), ", "))
%Y Cf. A215114, A213009, A215117, A215119.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Aug 03 2012
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