A329957 Expansion of q^(-2/3) * eta(q)^4 * eta(q^6)^4 / (eta(q^2)^3 * eta(q^3)^2) in powers of q.

1, -4, 5, -2, 2, -6, 8, -4, 2, -12, 13, -4, 4, -6, 10, -4, 5, -20, 10, -2, 6, -12, 18, -4, 6, -24, 16, -6, 4, -6, 20, -8, 7, -20, 10, -10, 4, -18, 24, -4, 6, -24, 29, -6, 8, -18, 20, -8, 4, -28, 20, -8, 10, -12, 18, -8, 8, -36, 26, -6, 12, -12, 20, -8, 8, -44

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

Euler transform of period 6 sequence [-4, -1, -2, -1, -4, -3, ...].

G.f.: Product_{k>=1} (1 - x^k)^4 * (1 - x^(6*k))^4 / ((1 - x^(2*k))^3 * (1 - x^(3*k))^2).

A329955(3*n + 2) = -2 * a(n).

Example

G.f. = 1 - 4*x + 5*x^2 - 2*x^3 + 2*x^4 - 6*x^5 + 8*x^6 - 4*x^7 + ...
G.f. = q^2 - 4*q^5 + 5*q^8 - 2*q^11 + 2*q^14 - 6*q^17 + 8*q^20 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^4 QPochhammer[ x^6]^5 / (QPochhammer[ x^2]^3 QPochhammer[ x^3]^2), {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^6 + A)^4 / (eta(x^2 + A)^3 * eta(x^3 + A)^2), n))};

Crossrefs

Cf. A329955.

Sequence in context: A337192 A255701 A085548 * A379183 A074459 A371747

Adjacent sequences: A329954 A329955 A329956 * A329958 A329959 A329960

Keyword

sign

Author

Michael Somos, Nov 29 2019

Status

approved