A329956 Expansion of q^(-1/3) * eta(q)^3 * eta(q^3) * eta(q^6) / eta(q^2)^2 in powers of q.

1, -3, 2, -2, 8, -7, 2, -4, 7, -10, 2, -2, 16, -10, 6, -4, 7, -16, 4, -6, 16, -15, 6, -4, 12, -10, 6, -6, 24, -20, 4, -4, 12, -21, 6, -6, 24, -26, 4, -8, 13, -10, 10, -8, 32, -10, 6, -12, 12, -32, 6, -4, 32, -26, 10, -4, 13, -30, 10, -10, 24, -20, 8, -8, 24

Offset

0,2

Links

Table of n, a(n) for n=0..64.

Formula

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

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

A329955(3*n + 1) = -a(n).

Example

G.f. = 1 - 3*x + 2*x^2 - 2*x^3 + 8*x^4 - 7*x^5 + 2*x^6 - 4*x^7 + ...
G.f. = q - 3*q^4 + 2*q^7 - 2*q^10 + 8*q^13 - 7*q^16 + 2*q^19 - 4*q^22 + ...

Mathematica

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

Prog

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

Crossrefs

Cf. A329955.

Sequence in context: A266275 A288536 A268864 * A242703 A141456 A137445

Adjacent sequences: A329953 A329954 A329955 * A329957 A329958 A329959

Keyword

sign

Author

Michael Somos, Nov 29 2019

Status

approved