A168479 G.f. satisfies: A(x/A(x)) = G(x)^3 where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.

1, 3, 21, 217, 2895, 46479, 857670, 17619348, 394066449, 9445681950, 239946999264, 6407385578778, 178774882463450, 5188026867995184, 156036783823130184, 4850255971984578744, 155467140310522090338

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

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

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

Self-convolution cube of A168478.

Example

G.f.: A(x) = 1 + 3*x + 21*x^2 + 217*x^3 + 2895*x^4 + 46479*x^5 +...
A(x/A(x)) = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 +...+ A001764(n+1)*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^3, x, serreverse(x/(A+x*O(x^n))))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(1+A*serreverse(x/(A+x*O(x^n))))^3); polcoeff(A, n)}

Crossrefs

Cf. A168478, A168449 (variant), A001764.

Sequence in context: A339644 A372159 A120972 * A158838 A236963 A107716

Adjacent sequences: A168476 A168477 A168478 * A168480 A168481 A168482

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2009

Status

approved