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!)
A105094 Expansion of 8 * (eta(q^2) / eta(q)^2)^8 in powers of q. 1
8, 128, 1152, 7680, 42112, 200448, 855552, 3345408, 12166272, 41609856, 134973184, 418023936, 1242729984, 3561814784, 9877810176, 26587137024, 69636039808, 177877244160, 443991342720, 1084762764800, 2598075516672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)

Richard E. Borcherds, Automorphic forms with singularities on Grassmannians, arXiv:alg-geom/9609022, 1996-1997; Invent. Math. 132 (1998), 491-562.

FORMULA

Expansion of 8 / phi(-q)^8 in powers of q where phi() is a Ramanujan theta function. - Michael Somos, Jun 08 2012

a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(15/4) * n^(11/4)). - Vaclav Kotesovec, Nov 14 2015

EXAMPLE

8 + 128*q + 1152*q^2 + 7680*q^3 + 42112*q^4 + 200448*q^5 + 855552*q^6 + ...

MAPLE

gf:=8*product((1-q^(2*n))^8, n=1..100)/product((1-q^n)^16, n=1..100): s:=series(gf, q, 100): for k from 0 to 40 do printf(`%d, `, coeff(s, q, k)) od: # James A. Sellers, Apr 09 2005

MATHEMATICA

QP = QPochhammer; s = 8*(QP[q^2]/QP[q]^2)^8 + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 8 * eta(x^2 + A)^8 / eta(x + A)^16, n))} /* Michael Somos, Apr 09 2005 */

CROSSREFS

Sequence in context: A061549 A303471 A301998 * A208711 A242355 A305519

Adjacent sequences:  A105091 A105092 A105093 * A105095 A105096 A105097

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 07 2005

EXTENSIONS

More terms from Michael Somos, Apr 07 2005

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 1 09:39 EST 2021. Contains 349426 sequences. (Running on oeis4.)