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 A215114 G.f. satisfies: A(x) = x + 2*x^2 + x*A(A(A(x))). 4
 1, 3, 9, 81, 891, 11907, 184437, 3199581, 60932007, 1257133527, 27836230041, 656867748537, 16429561047891, 433686821472747, 12038953175046909, 350402975398982133, 10665927632978564895, 338769129913521564735, 11205026468737167058785 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The (1/3)-iteration of the g.f. equals an integer series (A215115). LINKS FORMULA G.f. satisfies: A(x) = G(x)/G(G(x)) - 1 - G(G(x)) where A(G(x)) = x. EXAMPLE G.f.: A(x) = x + 3*x^2 + 9*x^3 + 81*x^4 + 891*x^5 + 11907*x^6 + 184437*x^7 +... where A(A(A(x))) = x + 9*x^2 + 81*x^3 + 891*x^4 + 11907*x^5 + 184437*x^6 +... Related expansions. Let C(C(C(x))) = A(x), then C(x) is an integer series where: C(x) = x + x^2 + x^3 + 19*x^4 + 163*x^5 + 2269*x^6 + 34093*x^7 +... where the coefficients of C(x) are congruent to 1 modulo 9. PROG (PARI) {a(n)=local(A=x+3*x^2); for(i=1, n, A=x+2*x^2+x*subst(A, x, subst(A, x, A+x*O(x^n)))); polcoeff(A, n)} for(n=1, 31, print1(a(n), ", ")) CROSSREFS Cf. A215115, A213010, A215116, A215118. Sequence in context: A047912 A078684 A121858 * A032108 A216206 A038062 Adjacent sequences:  A215111 A215112 A215113 * A215115 A215116 A215117 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 03 2012 STATUS approved

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)