A279362 Expansion of psi(x)^2 * chi(-x^5) in powers of x where psi(), chi() are Ramanujan theta functions.

1, 2, 1, 2, 2, -1, 1, 1, -2, 0, 2, -1, -1, 2, -2, -1, 0, -2, -2, -2, 0, -1, 1, 0, 2, -2, -5, 0, -2, 0, 0, 1, -2, 0, 0, -3, -1, 0, 0, -2, 1, -1, 2, 2, 0, 0, 0, -2, -2, 0, 2, 2, -2, 0, -2, 2, 1, 1, 0, 0, 0, -1, 2, 0, 4, 0, 1, 2, 0, 2, -1, 0, 0, 2, -2, -2, 4, -1

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..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-1/24) * eta(q^2)^4 * eta(q^5) / (eta(q)^2 * eta(q^10)) in powers of q.

Euler transform of period 10 sequence [ 2, -2, 2, -2, 1, -2, 2, -2, 2, -2, ...].

Example

G.f. = 1 + 2*x + x^2 + 2*x^3 + 2*x^4 - x^5 + x^6 + x^7 - 2*x^8 + 2*x^10 + ...
G.f. = q + 2*q^25 + q^49 + 2*q^73 + 2*q^97 - q^121 + q^145 + q^169 - ...

Mathematica

a[ n_] := SeriesCoefficient[ x^(-1/4) / 4 EllipticTheta[ 2, 0, x^(1/2)]^2 QPochhammer[ x^5, x^10], {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^5 + A) / (eta(x + A)^2 * eta(x^10 + A)), n))};
(PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q^2)^4*eta(q^5)/(eta(q)^2*eta(q^10)))} \\ Altug Alkan, Mar 21 2018

Crossrefs

Sequence in context: A186713 A156263 A109672 * A214841 A025917 A135689

Adjacent sequences: A279359 A279360 A279361 * A279363 A279364 A279365

Keyword

sign

Author

Michael Somos, Dec 10 2016

Status

approved