A135467 Expansion of q^(-3/4) * eta(q)^2 * eta(q^2)^4 * eta(q^8)^4 / eta(q^4)^6 in powers of q.

1, -2, -5, 10, 13, -22, -30, 40, 60, -78, -101, 132, 170, -210, -273, 342, 409, -514, -625, 748, 917, -1102, -1300, 1570, 1863, -2186, -2589, 3034, 3540, -4148, -4838, 5584, 6489, -7500, -8621, 9958, 11417, -13046, -14960, 17066, 19417, -22122, -25119, 28450, 32253, -36478

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

T. Ishikawa, Congruences between binomial coefficients binom(2f,f) and Fourier coefficients of certain eta-products, Hiroshima Math. J. 22 (1992), no. 3, 583-590.

Formula

Euler transform of period 8 sequence [ -2, -6, -2, 0, -2, -6, -2, -4, ...]. - Michael Somos, Mar 01 2008

Example

q^3 - 2*q^7 - 5*q^11 + 10*q^15 + 13*q^19 - 22*q^23 - 30*q^27 + ...

Mathematica

QP = QPochhammer; s = QP[q]^2*QP[q^2]^4*(QP[q^8]^4/QP[q^4]^6) + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 27 2015, adapted from PARI *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^2 + A)^2 / eta(x^4 + A)^3 * eta(x^8 + A)^2)^2, n))} /* Michael Somos, Mar 01 2008 */

Crossrefs

Sequence in context: A190437 A190249 A188434 * A230550 A018571 A064233

Adjacent sequences: A135464 A135465 A135466 * A135468 A135469 A135470

Keyword

sign

Author

N. J. A. Sloane, Feb 07 2008

Status

approved