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A164614 Expansion of (chi(q) / chi^3(q^3))^2 in powers of q where chi() is a Ramanujan theta function. 5
1, 2, 1, -4, -8, -2, 14, 24, 6, -38, -63, -16, 92, 150, 36, -208, -329, -78, 440, 684, 160, -884, -1358, -312, 1710, 2592, 590, -3196, -4796, -1082, 5800, 8632, 1929, -10270, -15162, -3364, 17784, 26078, 5750, -30192, -44010, -9644, 50369, 73012, 15916, -82698, -119280, -25880, 133818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-2/3) * (eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 / (eta(q) * eta(q^4) * eta(q^6)^6))^2 in powers of q.

Euler transform of period 12 sequence [ 2, -2, -4, 0, 2, 4, 2, 0, -4, -2, 2, 0, ...].

Convolution square of A128111.

EXAMPLE

G.f. = 1 + 2*x + x^2 - 4*x^3 - 8*x^4 - 2*x^5 + 14*x^6 + 24*x^7 + 6*x^8 + ...

G.f. = q^2 + 2*q^5 + q^8 - 4*q^11 - 8*q^14 - 2*q^17 + 14*q^20 + 24*q^23 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[(QPochhammer[-q, q^2]/(QPochhammer[-q^3, q^6])^3)^2, {q, 0, n}]; (* Michael Somos, Sep 02 2015 *)(* Corrected by G. C. Greubel_, Aug 10 2017 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^6))^2, n))};

CROSSREFS

Cf. A128111.

Sequence in context: A340469 A128411 A216046 * A254102 A094511 A209060

Adjacent sequences:  A164611 A164612 A164613 * A164615 A164616 A164617

KEYWORD

sign

AUTHOR

Michael Somos, Aug 17 2009

STATUS

approved

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Last modified June 20 12:04 EDT 2021. Contains 345164 sequences. (Running on oeis4.)