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A260301 Expansion of f(-x^3)^3 * psi(x)^3 / psi(x^3)^2 in powers of x where phi(), f() are Ramanujan theta functions. 5
1, 3, 3, -1, -9, -12, -5, 6, 15, 3, -12, -12, 7, 42, 30, 4, -33, -48, 3, 18, 36, -18, -60, -24, -17, 63, 42, -1, -42, -84, 20, 30, 63, 36, -48, -24, -9, 114, 90, -14, -60, -120, -18, 42, 84, -12, -120, -48, 31, 129, 63, 16, -126, -156, -5, 48, 102, -54, -84 (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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of eta(q^2)^6 * eta(q^3)^5 / (eta(q)^3 * eta(q^6)^4) in powers of q.

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

G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 27648^(1/2) (t/I)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A261445.

EXAMPLE

G.f. = 1 + 3*x + 3*x^2 - x^3 - 9*x^4 - 12*x^5 - 5*x^6 + 6*x^7 + 15*x^8 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (1/2) x^(3/8) QPochhammer[ x^3]^3 EllipticTheta[ 2, 0, x^(1/2)]^3 / EllipticTheta[ 2, 0, x^(3/2)]^2, {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^6 * eta(x^3 + A)^5 / (eta(x + A)^3 * eta(x^6 + A)^4), n))};

CROSSREFS

Cf. A261445.

Sequence in context: A084145 A122919 A188513 * A216916 A157401 A143911

Adjacent sequences:  A260298 A260299 A260300 * A260302 A260303 A260304

KEYWORD

sign,changed

AUTHOR

Michael Somos, Nov 10 2015

STATUS

approved

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Last modified November 15 14:06 EST 2019. Contains 329149 sequences. (Running on oeis4.)