A164562 Taylor series coefficients of phi(-q^3)*phi(q)/phi(q^2), where phi is Euler's function

1, -1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 1, 0, -1, -1, 1, 1, -1, -1, 1, 0, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 2, 2, -1, -1, 1, 1, -1, -2, 1, 2, -2, -1, 2, 1, -2, -2, 2, 3, -2, -2, 2, 2, -2, -3, 2, 3, -3, -2, 2, 2, -3, -3, 3, 3, -3, -3, 3

Offset

0,40

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Wikipedia, Euler function

Formula

From Michael Somos, Jun 07 2012: (Start)

G.f.: phi(-q^3)*phi(q)/phi(q^2).

|a(n)|<2 for n<39. |a(n)|<3 for n<56.

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

Example

G.f. = 1 - x - x^5 - x^6 + x^7 + x^8 + x^11 - x^14 + x^16 - x^18 + x^19 - x^21 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^3] QPochhammer[ x] / QPochhammer[ x^2], {x, 0, n}]; (* Michael Somos, May 03 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff(eta(x + A) * eta(x^6 + A)^3 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))}; /* Michael Somos, Jun 07 2012 */

Crossrefs

Matches 0th through 11th terms of A113687, also related to the Euler function.

Sequence in context: A105551 A305195 A073772 * A058188 A333851 A335230

Adjacent sequences: A164559 A164560 A164561 * A164563 A164564 A164565

Keyword

sign

Author

Gary Hinger (ghinger(AT)gmail.com), Aug 16 2009

Status

approved