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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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 07 2005
EXTENSIONS
More terms from Michael Somos, Apr 07 2005
STATUS
approved

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Last modified April 24 13:55 EDT 2024. Contains 371958 sequences. (Running on oeis4.)