A279261 Expansion of q^(-1/3) * eta(q)^3 * eta(q^3)^3 / eta(q^2)^2 in powers of q.

1, -3, 2, -4, 14, -11, 6, -20, 21, -14, 10, -16, 38, -20, 14, -40, 43, -42, 16, -28, 62, -43, 22, -40, 74, -42, 26, -40, 64, -68, 28, -80, 98, -63, 34, -52, 110, -62, 32, -100, 133, -70, 42, -56, 108, -80, 46, -120, 112, -114, 50, -72, 158, -84, 54, -140, 183

Offset

0,2

Links

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

Formula

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

3 * a(n) = A260301(3*n + 1).

Example

G.f. = 1 - 3*x + 2*x^2 - 4*x^3 + 14*x^4 - 11*x^5 + 6*x^6 - 20*x^7 + ...
G.f. = q - 3*q^4 + 2*q^7 - 4*q^10 + 14*q^13 - 11*q^16 + 6*q^19 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^3 QPochhammer[ x^3]^3 / 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)^3 / eta(x^2 + A)^2, n))};

Crossrefs

Cf. A260301.

Sequence in context: A137824 A019321 A336435 * A185390 A361422 A369776

Adjacent sequences: A279258 A279259 A279260 * A279262 A279263 A279264

Keyword

sign

Author

Michael Somos, Dec 08 2016

Status

approved