OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
Euler transform of period 3 sequence [ 6, 6, 0, ...].
Given g.f. A(x), then B(x)=x*A(x)^2 satisfies 0=f(B(x), B(x^2)) where f(u,v)=u^3+v^3-u*v-24*u*v*(u+v)-729*u^2*v^2.
G.f.: (Product_{k>0} (1-x^(3*k))/(1-x^k))^6.
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (27 * 2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1-x^(3*k)) / (1-x^k))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2015 *)
CoefficientList[Series[(QPochhammer[q^3]/QPochhammer[q])^6, {q, 0, 50}], q] (* G. C. Greubel, Nov 02 2018 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^3+A)/eta(x+A))^6, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 09 2006
STATUS
approved