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A034951
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Expansion of eta(8z)*eta(16z)*theta_3(2z)*theta_3(4z).
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0
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1, 2, 2, 4, 1, -2, 2, -4, -2, 2, -8, -4, -1, -4, -6, 0, -4, -8, 10, -4, -6, 6, 2, 8, 9, -4, -6, 4, 4, 14, 2, 4, 4, 10, 8, -12, 14, -2, 8, 8, -11, -6, -4, 12, -2, -8, 0, -4, -2, -2, -6, 4, -16, -2, -6, -20, 2, 8, 2, -8, -7, -12, -12, -16, 12, -6, -8, 8, 10, -10, -16, 4, -12, 18, 18, -4, -2, 0, 18, 12, -16, 2, -8, 20, -9, 2, 18, -4, 28, -6, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Ono and Skinner, Ann. Math., 147 (1998), 453-470.
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FORMULA
| G.f.: Product_{k>0} (1-x^(2k))(1+x^k)^2(1-x^(4k))^3/(1+x^(4k)). - Michael Somos Sep 21 2005.
Euler transform of period 8 sequence [2, -1, 2, -5, 2, -1, 2, -4, ...]. - Michael Somos Sep 21 2005
Expansion of q^(-1/2)(eta(q^2)^3*eta(q^4)^4)/(eta(q)^2*eta(q^8)) in powers of q. - Michael Somos Sep 21 2005
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EXAMPLE
| q + 2*q^3 + 2*q^5 + 4*q^7 + q^9 - 2*q^11 + 2*q^13 - 4*q^15 - 2*q^17 + ...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3*eta(x^4+A)^4/eta(x+A)^2/eta(x^8+A), n))} /* Michael Somos Sep 21 2005 */
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CROSSREFS
| Sequence in context: A181633 A099320 A206714 * A064848 A175001 A205843
Adjacent sequences: A034948 A034949 A034950 * A034952 A034953 A034954
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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