login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258291 Expansion of q^(-1/4) * eta(q) * eta(q^2) * eta(q^6) / eta(q^3) in powers of q. 3
1, -1, -2, 2, -1, 0, 3, -1, 0, 2, -1, -4, 1, -1, 0, 2, -2, 0, 2, 0, -2, 4, -1, 0, 2, -1, 0, 2, -1, -4, 1, -2, 0, 0, -1, 0, 4, -1, -4, 2, 0, 0, 3, -1, 0, 2, -2, 0, 2, -1, 0, 4, 0, 0, 0, -2, -6, 2, -1, 0, 2, -1, 0, 0, -1, -4, 4, -1, 0, 2, -1, 0, 3, -1, 0, 0, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

FORMULA

Euler transform of period 6 sequence [ -1, -2, 0, -2, -1, -2, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 9 (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A258277.

G.f.: Product_{k>0} (1 - x^k) * (1 - x^(2*k)) * (1 + x^(3*k)).

a(3*n) = A002175(n). a(3*n + 1) = - A121444(n). a(9*n + 2) = -2 * A008441(n). a(9*n + 5) = a(9*n + 8) = 0.

EXAMPLE

G.f. = 1 - x - 2*x^2 + 2*x^3 - x^4 + 3*x^6 - x^7 + 2*x^9 - x^10 - 4*x^11 + ...

G.f. = q - q^5 - 2*q^9 + 2*q^13 - q^17 + 3*q^25 - q^29 + 2*q^37 - q^41 + ...

MATHEMATICA

QP := QPochhammer; CoefficientList[Series[QP[q]*QP[q^2]*QP[q^6]/QP[q^3], {q, 0, 50}], q]] (* G. C. Greubel, Aug 04 2018 *)

PROG

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

CROSSREFS

Cf. A002175, A008441, A121444, A258277.

Sequence in context: A190182 A068926 A276770 * A146527 A285099 A306754

Adjacent sequences:  A258288 A258289 A258290 * A258292 A258293 A258294

KEYWORD

sign

AUTHOR

Michael Somos, May 25 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)