A215114 G.f. satisfies: A(x) = x + 2*x^2 + x*A(A(A(x))).

1, 3, 9, 81, 891, 11907, 184437, 3199581, 60932007, 1257133527, 27836230041, 656867748537, 16429561047891, 433686821472747, 12038953175046909, 350402975398982133, 10665927632978564895, 338769129913521564735, 11205026468737167058785

Offset

1,2

Comments

The (1/3)-iteration of the g.f. equals an integer series (A215115).

Links

Table of n, a(n) for n=1..19.

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