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A226862 Expansion of phi(x^3) * f(-x^4) in powers of x where phi(), f() are Ramanujan theta functions. 2
1, 0, 0, 2, -1, 0, 0, -2, -1, 0, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, -2, -2, 0, 0, 2, -2, 0, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 0, 0 (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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-1/6) * eta(q^4) * eta(q^6)^5 / (eta(q^3) * eta(q^12))^2 in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (576 t)) = 384^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A226861.

G.f.: (Sum_{k in Z} x^(3*k^2)) * Product_{k>0} (1 - x^(4*k)).

a(4*n + 1) = a(4*n + 2) = 0. a(4*n) = A226289(n).

EXAMPLE

G.f. = 1 + 2*x^3 - x^4 - 2*x^7 - x^8 - 2*x^11 + 2*x^12 - 2*x^16 - x^20 + 2*x^23 + ...

G.f. = q + 2*q^19 - q^25 - 2*q^43 - q^49 - 2*q^67 + 2*q^73 - 2*q^97 - q^121 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^3] QPochhammer[ q^4], {q, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^5 / (eta(x^3 + A) * eta(x^12 + A))^2, n))};

CROSSREFS

Cf. A226289, A226861.

Sequence in context: A131962 A302236 A262929 * A226864 A257399 A168313

Adjacent sequences:  A226859 A226860 A226861 * A226863 A226864 A226865

KEYWORD

sign

AUTHOR

Michael Somos, Jun 20 2013

STATUS

approved

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Last modified September 20 15:34 EDT 2020. Contains 337265 sequences. (Running on oeis4.)