A034433 Expansion of q^(-3) * (eta(q) * eta(q^8))^8 in powers of q.

1, -8, 20, 0, -70, 64, 56, 0, -133, -96, 148, 0, 670, -512, -968, 0, 1077, 1680, -2064, 0, -2098, 768, 4400, 0, -1766, -8128, 7044, 0, 744, 4096, -4760, 0, -9780, 16344, -6652, 0, 7894, -13440, -10320, 0, 41923, -8736, -16780, 0, -5892, -6144, 14560, 0, -27886, -11056, 55940

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

Euler transform of period 8 sequence [ -8, -8, -8, -8, -8, -8, -8, -16, ...]. - Michael Somos, Nov 11 2007

a(4*n+3) = 0.

Example

q^3 - 8*q^4 + 20*q^5 - 70*q^7 + 64*q^8 + 56*q^9 - 133*q^11 - 96*q^12 + ...

Mathematica

QP = QPochhammer; s = (QP[q]*QP[q^8])^8 + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x + A) * eta(x^8 + A) )^8, n))} /* Michael Somos, Nov 11 2007 */

Crossrefs

-8 * A002288(n) = a(4*n-3).

Sequence in context: A124972 A161969 A000731 * A282942 A225912 A120081

Adjacent sequences: A034430 A034431 A034432 * A034434 A034435 A034436

Keyword

sign

Author

N. J. A. Sloane

Status

approved