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Search: id:A030209
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| A030209 |
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Expansion of (eta(q)*eta(q^2)*eta(q^3)*eta(q^6))^2 in powers of q. |
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+0
1
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| 1, -2, -3, 4, 6, 6, -16, -8, 9, -12, 12, -12, 38, 32, -18, 16, -126, -18, 20, 24, 48, -24, 168, 24, -89, -76, -27, -64, 30, 36, -88, -32, -36, 252, -96, 36, 254, -40, -114, -48, 42, -96, -52, 48, 54, -336, -96, -48, -87, 178, 378, 152, 198, 54, 72, 128, -60, -60, -660, -72, -538, 176, -144, 64, 228, 72, 884
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Expansion of a newform level 6 weight 4 and trivial character.
Identical to table 1, p. 493, of Alaca citation. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2007
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REFERENCES
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Saban Alaca and Kenneth Williams, Evaluation of the convolution sums..., Journal of Number Theory 124(2007)491-510.
M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
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LINKS
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Author?, Eta Products and Quotients which are Newforms.
W. Stein, Modular Forms Database.
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FORMULA
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Euler transform of period 6 sequence [ -2,-4,-4,-4,-2,-8,...]. - Michael Somos Feb 13 2006
a(n) is multiplicative with a(p^e)=(-p)^e if p<5, a(p^e) = a(p)a(p^(e-1)) -p^3*a(p^(e-2)) otherwise. - Michael Somos Feb 13 2006
G.f.: x*(Product_{k>0} (1-x^k)(1-x^(2k))(1-x^(3k))(1-x^(6k)))^2.
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EXAMPLE
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q -2*q^2 -3*q^3 +4*q^4 +6*q^5 +6*q^6 -16*q^7 -8*q^8 +9*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)*eta(x^2+A)*eta(x^3+A)*eta(x^6+A))^2, n))} /* Michael Somos Feb 14 2006 */
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CROSSREFS
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Sequence in context: A000793 A062163 A002729 this_sequence A138588 A143102 A013944
Adjacent sequences: A030206 A030207 A030208 this_sequence A030210 A030211 A030212
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KEYWORD
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sign,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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