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A168653 G.f. satisfies: A(x*A(x)) = G(x) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764. 0
1, 1, 2, 6, 21, 82, 340, 1478, 6622, 30433, 142331, 676203, 3248579, 15776459, 77196573, 380849394, 1888606247, 9430534212, 47236684433, 238214461960, 1202007809362, 6116704517639, 30997312336216, 159384351652358 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f. satisfies: A(x) = 1 + A(x)^3*Series_Reversion(x*A(x)).

G.f. satisfies: A( x*(1-x)^2*A(x*(1-x)^2) ) = 1/(1-x).

G.f. satisfies: A( (x/(1+x)^3)*A(x/(1+x)^3) ) = 1 + x.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 82*x^5 + 340*x^6 +...

A(x*A(x)) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...

PROG

(PARI) {a(n)=local(A=1+x, F=sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F, x, serreverse(x*(A+x*O(x^n))^1))); polcoeff(A, n)}

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+A^3*serreverse(x*(A+x*O(x^n)))); polcoeff(A, n)}

CROSSREFS

Cf. A154677, A168478, A168448, A001764.

Sequence in context: A150218 A150219 A150220 * A279567 A281784 A032347

Adjacent sequences:  A168650 A168651 A168652 * A168654 A168655 A168656

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 06 2009

STATUS

approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)