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A261444 Expansion of f(x^3)^2 * f(-x^6)^2 / f(-x^2) in powers of x where f() is a Ramanujan theta function. 5
1, 0, 1, 2, 2, 2, 0, 4, 2, 0, 1, 4, 4, 2, 2, 4, 5, 0, 2, 2, 6, 4, 2, 4, 6, 0, 0, 6, 4, 2, 4, 8, 7, 0, 2, 10, 4, 6, 0, 4, 6, 0, 1, 6, 8, 6, 4, 8, 4, 0, 4, 8, 10, 4, 2, 8, 8, 0, 2, 6, 12, 4, 4, 8, 8, 0, 5, 8, 6, 4, 0, 8, 14, 0, 2, 10, 8, 10, 2, 8, 11, 0, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-2/3) * eta(q^6)^8 / (eta(q^2) * eta(q^3)^2 * eta(q^12)^2) in powers of q.

Euler transform of period 12 sequence [ 0, 1, 2, 1, 0, -5, 0, 1, 2, 1, 0, -3, ...].

a(n) = A261426(2*n + 1).

EXAMPLE

G.f. = 1 + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8 + x^10 + ...

G.f. = q^2 + q^8 + 2*q^11 + 2*q^14 + 2*q^17 + 4*q^23 + 2*q^26 + ...

MATHEMATICA

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

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A)^8 / (eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^12 + A)^2), n))};

CROSSREFS

Cf. A261426.

Sequence in context: A103223 A091399 A263527 * A000091 A155123 A125938

Adjacent sequences:  A261441 A261442 A261443 * A261445 A261446 A261447

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 18 2015

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)