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%I #4 Aug 03 2012 14:37:56
%S 1,5,25,625,18125,628125,25390625,1158515625,58308203125,
%T 3190470703125,187941103515625,11832996337890625,791834056298828125,
%U 56063448811767578125,4184231129351806640625,328154000925299072265625,26970505516268341064453125,2317475342690856231689453125
%N G.f. satisfies: A(x) = x + 4*x^2 + x*A(A(A(A(A(x))))).
%C The (1/5)-iteration of the g.f. equals an integer series (A215119).
%e G.f.: A(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 +...
%e where
%e A(A(A(A(x)))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 +...
%e Related expansions.
%e Let E(E(E(E(E(x))))) = A(x), then E(x) is an integer series where:
%e E(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 +...
%e where the coefficients of E(x) are congruent to 1 modulo 100.
%o (PARI) {a(n)=local(A=x+4*x^2); for(i=1,n,A=x+4*x^2+x*subst(A,x,subst(A,x,subst(A,x,subst(A,x,A+x*O(x^n)))))); polcoeff(A, n)}
%o for(n=1, 31, print1(a(n), ", "))
%Y Cf. A215119, A213010, A215114, A215116.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 03 2012
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