A134414 Expansion of eta(q)^2 / (eta(q^2) * eta(q^4)^6) in powers of q.

1, -2, 0, 0, 8, -12, 0, 0, 39, -56, 0, 0, 152, -208, 0, 0, 513, -684, 0, 0, 1560, -2032, 0, 0, 4382, -5616, 0, 0, 11552, -14592, 0, 0, 28899, -36088, 0, 0, 69168, -85500, 0, 0, 159372, -195312, 0, 0, 355224, -431984, 0, 0, 768885, -928720, 0, 0, 1621296, -1946352, 0, 0, 3339201

Offset

-1,2

Links

Seiichi Manyama, Table of n, a(n) for n = -1..1000

K. Bringmann and K. Ono, An arithmetic formula for the partition function, Proc Am. Math. Soc. 135 (2007), 3507-3514. see p. 3507 Equ. (1.2).

Formula

Euler transform of period 4 sequence [ -2, -1, -2, 5, ...].

a(4*n+1) = a(4*n+2) = 0.

G.f.: x^(-1) * Product_{k>0} (1 - x^k) / ((1 + x^k) * (1 - x^(4*k))^6).

Example

1/q - 2 + 8*q^3 - 12*q^4 + 39*q^7 - 56*q^8 + 152*q^11 - 208*q^12 + ...

Mathematica

QP = QPochhammer; s = QP[q]^2/(QP[q^2]*QP[q^4]^6) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 27 2015 *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^2 / (eta(x^2 + A) * eta(x^4 + A)^6), n))}

Crossrefs

A134415(n) = a(4*n-1). -2 * A134416(n) = a(4*n).

Sequence in context: A332473 A235789 A236925 * A113036 A000425 A230878

Adjacent sequences: A134411 A134412 A134413 * A134415 A134416 A134417

Keyword

sign

Author

Michael Somos, Oct 26 2007

Status

approved