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Search: id:A029769
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| A029769 |
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eta(2z)^12/theta_3(z)^3. |
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+0
2
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| 1, -6, 12, -8, 0, 12, -48, 48, -15, 60, -12, -96, 0, -120, 240, 64, 96, -234, -156, 0, 0, 444, -240, -96, -335, 420, 144, 384, 0, -600, -480, -384, 672, -264, 840, 120, 0, -348, 912, -480, -768, -168, -684, 96, 0, 1416, -672, 768, 673, 510, -2328, 0, 0, 144, 1200, 960, -1248, -1332, 1500, -1920
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Shimura, Modular forms of half-integral weight, pp. 57-74 of Modular Functions of One Variable I (Antwerp 1972), Lect. Notes Math. 320 (1973).
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FORMULA
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a(8n+5)=0.
Expansion of eta(q)^6* eta(q^4)^6/ eta(q^2)^3 in powers of q.
Euler transform of period 4 sequence [ -6, -3, -6, -9, ...].
G.f. is Fourier series of a weight 9/2 level 4 cusp form. f(-1/ (4 t)) = (i (-2 t)^9)^(1/2) f(t) where q = exp(2 pi i t). - Michael Somos Jul 25 2007
G.f.: x* (Product_{k>0} (1-x^k)^2* (1+x^(2k))* (1-x^(4k)))^3.
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EXAMPLE
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q - 6*q^2 + 12*q^3 - 8*q^4 + 12*q^6 - 48*q^7 + 48*q^8 - 15*q^9 + ...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<1, 0, n--; A= x*O(x^n); polcoeff( eta(x+A)^6* eta(x^4+A)^6/ eta(x^2+A)^3, n))} /* Michael Somos Apr 24 2004 */
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CROSSREFS
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Sequence in context: A122859 A050496 A103698 this_sequence A074590 A105730 A005875
Adjacent sequences: A029766 A029767 A029768 this_sequence A029770 A029771 A029772
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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