A260295 Expansion of f(-x^2)^3 * f(-x^6)^3 / f(-x)^2 in powers of x where f() is a Ramanujan theta function.

1, 2, 2, 4, 5, 6, 7, 6, 9, 8, 11, 14, 10, 14, 15, 16, 14, 14, 19, 20, 21, 22, 21, 20, 28, 26, 24, 22, 29, 30, 26, 32, 26, 38, 35, 36, 37, 28, 39, 40, 41, 42, 34, 40, 43, 42, 47, 42, 49, 50, 56, 44, 42, 54, 55, 62, 57, 46, 50, 60, 56, 62, 50, 70, 60, 56, 74, 54

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^(-11/12) * eta(q^2)^3 * eta(q^6)^3 / eta(q)^2 in powers of q.

Euler transform of period 6 sequence [2, -1, 2, -1, 2, -4, ...]. - Michael Somos, Aug 01 2018

Example

G.f. = 1 + 2*x + 2*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 6*x^7 + ...
G.f. = q^11 + 2*q^23 + 2*q^35 + 4*q^47 + 5*q^59 + 6*q^71 + 7*q^83 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^3 QPochhammer[ x^6]^3 / QPochhammer[ x]^2, {x, 0, n}];

Prog

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

Crossrefs

Sequence in context: A059015 A325108 A329474 * A024683 A244017 A339022

Adjacent sequences: A260292 A260293 A260294 * A260296 A260297 A260298

Keyword

nonn

Author

Michael Somos, Oct 07 2015

Status

approved