A121592 Expansion of (eta(q)eta(q^9)/eta(q^3)^2)^6 in powers of q.

1, -6, 9, 22, -102, 108, 221, -858, 810, 1476, -5262, 4572, 7802, -26112, 21519, 34918, -111870, 88452, 138332, -427980, 327852, 497592, -1497666, 1117692, 1655719, -4869876, 3556791, 5161808, -14891262, 10677096, 15226658, -43198938, 30485268

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

Euler transform of period 9 sequence [ -6, -6, 6, -6, -6, 6, -6, -6, 0, ...].

G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^3+v^3-u*v+12*u*v*(u+v)+27*u^2*v^2.

G.f.: x*(Product_{k>0} (1-x^k)(1-x^(9k))/(1-x^(3k))^2)^6.

Mathematica

QP = QPochhammer; s = (QP[q]*(QP[q^9]/QP[q^3]^2))^6 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)

Prog

(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^5+A)/eta(x+A))^6, n))}

Crossrefs

Cf. A131985.

Sequence in context: A006132 A033705 A033704 * A295726 A034718 A215528

Adjacent sequences: A121589 A121590 A121591 * A121593 A121594 A121595

Keyword

sign

Author

Michael Somos, Aug 09 2006

Status

approved