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A260057 Expansion of f(-x, -x^5)^3 / (f(x, x^5) * f(-x^2, -x^2)^2) in powers of x where f(, ) is Ramanujan's general theta function. 3
1, -4, 11, -24, 48, -92, 170, -304, 526, -884, 1451, -2336, 3700, -5772, 8876, -13472, 20207, -29988, 44072, -64184, 92680, -132760, 188758, -266512, 373838, -521152, 722266, -995432, 1364684, -1861548, 2527224, -3415344, 4595497, -6157700, 8218050, -10925848 (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..2500

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of f(-x) * psi(x^3)^3 / (f(x)^3 * psi(-x^3)) in powers of x where psi(), f() are Ramanujan theta functions.

Expansion of q^(-2/3) * eta(q)^4 * eta(q^4)^3 * eta(q^6)^7 / (eta(q^2)^9 * eta(q^3)^4 * eta(q^12)) in powers of q.

Euler transform of period 12 sequence [-4, 5, 0, 2, -4, 2, -4, 2, 0, 5, -4, 0, ...].

2 * a(n) = A260215(3*n + 2).

a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/3)) / (4*3^(5/4)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017

EXAMPLE

G.f. = 1 - 4*x + 11*x^2 - 24*x^3 + 48*x^4 - 92*x^5 + 170*x^6 - 304*x^7 + ...

G.f. = q^2 - 4*q^5 + 11*q^8 - 24*q^11 + 48*q^14 - 92*q^17 + 170*q^20 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ 2^(-5/2) x^(-3/4) QPochhammer[ x] / QPochhammer[ -x]^3 EllipticTheta[ 2, 0, x^(3/2)]^3 / EllipticTheta[ 2, Pi/4, x^(3/2)], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^4 + A)^3 * eta(x^6 + A)^7 / (eta(x^2 + A)^9 * eta(x^3 + A)^4 * eta(x^12 + A)), n))};

CROSSREFS

Cf. A260215.

Sequence in context: A192748 A143075 A290707 * A260150 A258472 A007678

Adjacent sequences:  A260054 A260055 A260056 * A260058 A260059 A260060

KEYWORD

sign

AUTHOR

Michael Somos, Nov 08 2015

STATUS

approved

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)