A262158 Expansion of psi(x^3)^3 * psi(x^2) / psi(x)^4 in powers of x where psi() is a Ramanujan theta function

1, -4, 11, -25, 53, -107, 205, -377, 672, -1166, 1975, -3275, 5333, -8544, 13484, -20994, 32288, -49100, 73888, -110115, 162635, -238196, 346123, -499244, 715110, -1017610, 1439098, -2023208, 2828543, -3933466, 5442352, -7493714, 10270711, -14014683, 19042562

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-7/8) * eta(q)^4 * eta(q^4)^2 * eta(q^6)^6 / (eta(q^2)^9 * eta(q^3)^3) in powers of q.

Euler transform of period 12 sequence [-4, 5, -1, 3, -4, 2, -4, 3, -1, 5, -4, 0, ...].

Example

G.f. = 1 - 4*x + 11*x^2 - 25*x^3 + 53*x^4 - 107*x^5 + 205*x^6 + ...
G.f. = q^7 - 4*q^15 + 11*q^23 - 25*q^31 + 53*q^39 - 107*q^47 + ...

Mathematica

a[ n_] := SeriesCoefficient[ x^(-7/8) EllipticTheta[ 2 , 0, x^(3/2)]^3 EllipticTheta[ 2 , 0, x] / EllipticTheta[ 2 , 0, x^(1/2)]^4, {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)^2 * eta(x^6 + A)^6 / (eta(x^2 + A)^9 * eta(x^3 + A)^3), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^4*eta(q^4)^2*eta(q^6)^6/(eta(q^2)^9*eta(q^3)^3)) \\ Altug Alkan, Jul 31 2018

Crossrefs

Sequence in context: A290986 A209232 A266337 * A156127 A178742 A202088

Adjacent sequences: A262155 A262156 A262157 * A262159 A262160 A262161

Keyword

sign

Author

Michael Somos, Sep 13 2015

Status

approved