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A262056 Expansion of phi(q^2) / phi(-q^3) in powers of q where phi() is a Ramanujan theta function. 1
1, 0, 2, 2, 0, 4, 4, 0, 10, 8, 0, 20, 14, 0, 36, 24, 0, 64, 42, 0, 108, 68, 0, 176, 108, 0, 280, 170, 0, 436, 260, 0, 666, 392, 0, 1000, 584, 0, 1480, 856, 0, 2160, 1240, 0, 3116, 1780, 0, 4448, 2526, 0, 6286, 3552, 0, 8804, 4956, 0, 12228, 6856, 0, 16852 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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^4)^5 * eta(q^6) / (eta(q^2)^2 * eta(q^3)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 24 sequence [ 0, 2, 2, -3, 0, 3, 0, -1, 2, 2, 0, -2, 0, 2, 2, -1, 0, 3, 0, -3, 2, 2, 0, 0, ...].

a(n) = A143068(2*n). a(3*n + 1) = 0.

EXAMPLE

G.f. = 1 + 2*q^2 + 2*q^3 + 4*q^5 + 4*q^6 + 10*q^8 + 8*q^9 + 20*q^11 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^2] / EllipticTheta[ 4, 0, q^3], {q, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^5 * eta(x^6 + A) / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^8 + A)^2), n))};

CROSSREFS

Cf. A143068.

Sequence in context: A168090 A078029 A078030 * A264628 A241320 A073469

Adjacent sequences:  A262053 A262054 A262055 * A262057 A262058 A262059

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 09 2015

STATUS

approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)