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A121596
Expansion of q^(-1/2)(eta(q^3)/eta(q))^6 in powers of q.
5
1, 6, 27, 92, 279, 756, 1913, 4536, 10260, 22220, 46479, 94176, 185749, 357426, 673056, 1242404, 2252772, 4017816, 7058609, 12228060, 20911230, 35330324, 59023728, 97568712, 159693831, 258941124, 416181510, 663337512, 1048935414
OFFSET
0,2
LINKS
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
Sequence in context: A052267 A038166 A327384 * A264026 A341385 A344100
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 09 2006
STATUS
approved