A262157 Expansion of psi(x^3)^3 / (psi(x)^2 * psi(x^2)) in powers of x where psi() is a Ramanujan theta function.

1, -2, 2, -1, 3, -8, 9, -7, 13, -26, 29, -23, 38, -72, 79, -67, 103, -178, 196, -170, 248, -409, 447, -403, 564, -883, 966, -886, 1204, -1819, 1984, -1861, 2465, -3600, 3926, -3733, 4846, -6893, 7507, -7243, 9238, -12822, 13961, -13609, 17104, -23263, 25309

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^(-15/24) * eta(q)^2 * eta(q^6)^6 / (eta(q^2)^3 * eta(q^3)^3 * eta(q^4)^2) in powers of q.

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

Example

G.f. = 1 - 2*x + 2*x^2 - x^3 + 3*x^4 - 8*x^5 + 9*x^6 - 7*x^7 + ...
G.f. = q^5 - 2*q^13 + 2*q^21 - q^29 + 3*q^37 - 8*q^45 + 9*q^53 + ...

Mathematica

a[ n_] := SeriesCoefficient[ x^(-5/8) EllipticTheta[ 2 , 0, x^(3/2)]^3 / (EllipticTheta[ 2 , 0, x^(1/2)]^2 EllipticTheta[ 2 , 0, x]), {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^6 + A)^6 / (eta(x^2 + A)^3 * eta(x^3 + A)^3 * eta(x^4 + A)^2), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^6)^6/(eta(q^2)^3*eta(q^3)^3*eta(q^4)^2)) \\ Altug Alkan, Jul 31 2018

Crossrefs

Sequence in context: A295736 A136203 A113326 * A090447 A241186 A258222

Adjacent sequences: A262154 A262155 A262156 * A262158 A262159 A262160

Keyword

sign

Author

Michael Somos, Sep 13 2015

Status

approved