A121596 Expansion of q^(-1/2)(eta(q^3)/eta(q))^6 in powers of q.

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

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

Sequence in context: A052267 A038166 A327384 * A264026 A341385 A344100

Adjacent sequences: A121593 A121594 A121595 * A121597 A121598 A121599

Keyword

nonn

Author

Michael Somos, Aug 09 2006

Status

approved