A168478 G.f. satisfies: A(x/A(x)^3) = G(x) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

1, 1, 6, 60, 803, 13071, 244917, 5101603, 115451307, 2794682082, 71579132742, 1924722618873, 54022011952266, 1575777019075715, 47606721776494443, 1485688929610479498, 47790055655273649449, 1581727833458617151379

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

G.f. satisfies: A( (x*(1-x)^2)/A(x*(1-x)^2)^3 ) = 1/(1-x).

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

Example

G.f.: A(x) = 1 + x + 6*x^2 + 60*x^3 + 803*x^4 + 13071*x^5 +...
A(x/A(x)^3) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...+ A001764(n)*x^n +...

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))^3))); 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))^3)); polcoeff(A, n)}

Crossrefs

Cf. A168479 (cube), A168448 (variant), A001764.

Sequence in context: A120973 A259606 A302102 * A101470 A367472 A066151

Adjacent sequences: A168475 A168476 A168477 * A168479 A168480 A168481

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2009

Status

approved