A196864 G.f. A(x) satisfies: A(x)^3 + A(-x)^3 = 2 and A(x)^-3 - A(-x)^-3 = -18*x.

1, 3, -9, -198, 1188, 30213, -220239, -5945238, 47541735, 1325876283, -11192990913, -318640183182, 2787445591416, 80483342059224, -722019579525288, -21063846331387728, 192542324985927324, 5661585516173303268, -52508399485861250604, -1553593208517770295816

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: ( 2*(sqrt(1+4*3^4*x^2) + 2*3^2*x)/(sqrt(1+4*3^4*x^2) + 1) )^(1/6).

Example

 G.f.: A(x) = 1 + 3*x - 9*x^2 - 198*x^3 + 1188*x^4 + 30213*x^5 +...
where
A(x)^3 = 1 + 9*x - 729*x^3 + 118098*x^5 - 23914845*x^7 + 5423886846*x^9 +...
A(x)^-3 = 1 - 9*x + 81*x^2 - 6561*x^4 + 1062882*x^6 - 215233605*x^8 +...

Prog

 (PARI) {a(n)=local(A=[1, 3]); for(k=2, n, A=concat(A, 0); if(k%2==0, A[#A]=-Vec(Ser(A)^3)[#A]/3, A[#A]=Vec(Ser(A)^-3)[#A]/3)); A[n+1]}
(PARI) {a(n)=local(X=x+x*O(x^n)); polcoeff((2*(sqrt(1+4*3^4*X^2) + 2*3^2*x)/(sqrt(1+4*3^4*X^2) + 1) )^(1/6), n)}

Crossrefs

Cf. A196865, A193618, A193619, A196866, A196867, A196868, A196869.

Sequence in context: A061963 A174603 A062228 * A279834 A091409 A027891

Adjacent sequences: A196861 A196862 A196863 * A196865 A196866 A196867

Keyword

sign

Author

Paul D. Hanna, Oct 06 2011

Status

approved