A255317 Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions.

1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1

Offset

0,8

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 psi(x^6) * f(x, x^2) in powers of x where psi(), f() are Ramanujan theta functions.

Expansion of q^(-19/24) * eta(q^2) * eta(q^3)^2 * eta(q^12)^2 / (eta(q) * eta(q^6)^2) in powers of q.

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

Example

G.f. = 1 + x + x^2 + x^5 + x^6 + 2*x^7 + x^8 + x^11 + x^12 + x^13 + ...
G.f. = q^19 + q^43 + q^67 + q^139 + q^163 + 2*q^187 + q^211 + q^283 + ...

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A118229 A172250 A309047 * A309168 A179229 A117201

Adjacent sequences: A255314 A255315 A255316 * A255318 A255319 A255320

Keyword

nonn

Author

Michael Somos, Feb 21 2015

Status

approved