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A246608 Expansion of phi(-q) * phi(-q^4)^4 in powers of q where phi() is a Ramanujan theta function. 1
1, -2, 0, 0, -6, 16, 0, 0, 8, -50, 0, 0, 16, 80, 0, 0, -38, -96, 0, 0, -16, 160, 0, 0, 48, -242, 0, 0, 64, 240, 0, 0, -56, -288, 0, 0, -150, 400, 0, 0, 112, -384, 0, 0, 112, 496, 0, 0, -112, -674, 0, 0, -80, 560, 0, 0, 160, -672, 0, 0, 192, 880, 0, 0, -294 (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 * eta(q^4)^8 / (eta(q^2) * eta(q^8)^4) in powers of q.

a(4*n) = A245643(n). a(4*n + 1) = -2 * A244276(n). a(4*n + 2) = a(4*n + 3) = 0.

EXAMPLE

G.f. = 1 - 2*q - 6*q^4 + 16*q^5 + 8*q^8 - 50*q^9 + 16*q^12 + 80*q^13 + ...

MATHEMATICA

a[n_]:= SeriesCoefficient[EllipticTheta[3, 0, -q]*EllipticTheta[3, 0, -q^4 ]^4, {q, 0, n}]; (* corrected by G. C. Greubel, Mar 15 2018 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^8 / (eta(x^2 + A) * eta(x^8 + A)^4), n))};

(MAGMA) A := Basis( ModularForms( Gamma0(8), 5/2), 68); A[1] - 2*A[2];

CROSSREFS

Cf. A244276, A245643.

Sequence in context: A244133 A244142 A161800 * A100344 A094596 A143024

Adjacent sequences:  A246605 A246606 A246607 * A246609 A246610 A246611

KEYWORD

sign,changed

AUTHOR

Michael Somos, Sep 01 2014

STATUS

approved

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Last modified November 18 12:35 EST 2019. Contains 329261 sequences. (Running on oeis4.)