A196865 G.f. A(x) satisfies: A(x)^-3 + A(-x)^-3 = 2 and A(x)^3 - A(-x)^3 = 18*x.

1, 3, 18, -117, -1971, 16119, 343278, -3036528, -71818164, 661017348, 16593480504, -156436510221, -4080815440497, 39095628518637, 1047594828442626, -10152600834566916, -277489726161424569, 2712640349690579349, 75279129630178436622, -740885355955719640809

Offset

0,2

Links

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

Formula

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

Example

G.f.: A(x) = 1 + 3*x + 18*x^2 - 117*x^3 - 1971*x^4 + 16119*x^5 +...
where
A(x)^3 = 1 + 9*x + 81*x^2 - 6561*x^4 + 1062882*x^6 - 215233605*x^8 +...
A(x)^-3 = 1 - 9*x + 729*x^3 - 118098*x^5 + 23914845*x^7 - 5423886846*x^9 +...

Prog

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

Crossrefs

Cf. A196864, A193618, A193619, A196866, A196867, A196868, A196869.

Sequence in context: A074566 A291076 A113328 * A153394 A334682 A320616

Adjacent sequences: A196862 A196863 A196864 * A196866 A196867 A196868

Keyword

sign

Author

Paul D. Hanna, Oct 06 2011

Status

approved