A168653 G.f. satisfies: A(x*A(x)) = G(x) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

1, 1, 2, 6, 21, 82, 340, 1478, 6622, 30433, 142331, 676203, 3248579, 15776459, 77196573, 380849394, 1888606247, 9430534212, 47236684433, 238214461960, 1202007809362, 6116704517639, 30997312336216, 159384351652358

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