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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293306 Expansion of (eta(q)eta(q^3))/eta(q^2)^2 in powers of q. 4
1, -1, 1, -3, 4, -5, 6, -9, 13, -16, 20, -27, 36, -44, 54, -69, 88, -107, 130, -162, 200, -240, 288, -351, 426, -507, 602, -723, 864, -1019, 1200, -1422, 1681, -1968, 2300, -2700, 3160, -3674, 4266, -4965, 5768, -6665, 7692, -8892, 10260, -11792, 13536, -15552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Product_{i>0} (1 + Sum_{j>0} (-1)^j*j*q^(j*i)).

a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)/3) / (6*n^(3/4)). - Vaclav Kotesovec, Oct 05 2017

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 - x^k) * (1 - x^(3*k)) / (1 - x^(2*k))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2017 *)

CROSSREFS

Main diagonal of A293305.

Cf. A122792.

Sequence in context: A105857 A103055 A128995 * A014101 A039035 A065798

Adjacent sequences:  A293303 A293304 A293305 * A293307 A293308 A293309

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 05 2017

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 July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)