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%I #38 Apr 19 2018 03:54:46
%S 8,128,1152,7680,42112,200448,855552,3345408,12166272,41609856,
%T 134973184,418023936,1242729984,3561814784,9877810176,26587137024,
%U 69636039808,177877244160,443991342720,1084762764800,2598075516672
%N Expansion of 8 * (eta(q^2) / eta(q)^2)^8 in powers of q.
%H G. C. Greubel, <a href="/A105094/b105094.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from Vincenzo Librandi)
%H Richard E. Borcherds, <a href="https://arxiv.org/abs/alg-geom/9609022">Automorphic forms with singularities on Grassmannians</a>, arXiv:alg-geom/9609022, 1996-1997; Invent. Math. 132 (1998), 491-562.
%F Expansion of 8 / phi(-q)^8 in powers of q where phi() is a Ramanujan theta function. - _Michael Somos_, Jun 08 2012
%F a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(15/4) * n^(11/4)). - _Vaclav Kotesovec_, Nov 14 2015
%e 8 + 128*q + 1152*q^2 + 7680*q^3 + 42112*q^4 + 200448*q^5 + 855552*q^6 + ...
%p 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
%t QP = QPochhammer; s = 8*(QP[q^2]/QP[q]^2)^8 + O[q]^30; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 14 2015 *)
%o (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 */
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Apr 07 2005
%E More terms from _Michael Somos_, Apr 07 2005
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