A261444 Expansion of f(x^3)^2 * f(-x^6)^2 / f(-x^2) in powers of x where f() is a Ramanujan theta function.

1, 0, 1, 2, 2, 2, 0, 4, 2, 0, 1, 4, 4, 2, 2, 4, 5, 0, 2, 2, 6, 4, 2, 4, 6, 0, 0, 6, 4, 2, 4, 8, 7, 0, 2, 10, 4, 6, 0, 4, 6, 0, 1, 6, 8, 6, 4, 8, 4, 0, 4, 8, 10, 4, 2, 8, 8, 0, 2, 6, 12, 4, 4, 8, 8, 0, 5, 8, 6, 4, 0, 8, 14, 0, 2, 10, 8, 10, 2, 8, 11, 0, 6, 6, 6

Offset

0,4

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^(-2/3) * eta(q^6)^8 / (eta(q^2) * eta(q^3)^2 * eta(q^12)^2) in powers of q.

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

a(n) = A261426(2*n + 1).

Example

G.f. = 1 + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8 + x^10 + ...
G.f. = q^2 + q^8 + 2*q^11 + 2*q^14 + 2*q^17 + 4*q^23 + 2*q^26 + ...

Mathematica

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

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A)^8 / (eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^12 + A)^2), n))};

Crossrefs

Cf. A261426.

Sequence in context: A091399 A350951 A263527 * A000091 A155123 A125938

Adjacent sequences: A261441 A261442 A261443 * A261445 A261446 A261447

Keyword

nonn

Author

Michael Somos, Aug 18 2015

Status

approved