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A105094
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Expansion of 8 * (eta(q^2) / eta(q)^2)^8 in powers of q.
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1
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8, 128, 1152, 7680, 42112, 200448, 855552, 3345408, 12166272, 41609856, 134973184, 418023936, 1242729984, 3561814784, 9877810176, 26587137024, 69636039808, 177877244160, 443991342720, 1084762764800, 2598075516672
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OFFSET
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0,1
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LINKS
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FORMULA
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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
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EXAMPLE
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8 + 128*q + 1152*q^2 + 7680*q^3 + 42112*q^4 + 200448*q^5 + 855552*q^6 + ...
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MAPLE
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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
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MATHEMATICA
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QP = QPochhammer; s = 8*(QP[q^2]/QP[q]^2)^8 + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015 *)
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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