Search: id:A030209
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%I A030209
%S A030209 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,
%T A030209 76,27,64,30,36,88,32,36,252,96,36,254,40,114,48,42,96,52,48,54,336,96,
%U A030209 48,87,178,378,152,198,54,72,128,60,60,660,72,538,176,144,64,228,72,884
%V A030209 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,
%W A030209 -27,-64,30,36,-88,-32,-36,252,-96,36,254,-40,-114,-48,42,-96,-52,48,54,
               -336,-96,-48,
%X A030209 -87,178,378,152,198,54,72,128,-60,-60,-660,-72,-538,176,-144,64,228,72,
               884
%N A030209 Expansion of (eta(q)*eta(q^2)*eta(q^3)*eta(q^6))^2 in powers of q.
%C A030209 Expansion of a newform level 6 weight 4 and trivial character.
%C A030209 Identical to table 1, p. 493, of Alaca citation. - Jonathan Vos Post 
               (jvospost3(AT)gmail.com), May 24 2007
%D A030209 Saban Alaca and Kenneth Williams, Evaluation of the convolution sums..., 
               Journal of Number Theory 124(2007)491-510.
%D A030209 M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
%H A030209 Author?, <a href="http://www.math.okstate.edu/~loriw/degree2/degree2hm/
               eta2/eta2.html">Eta Products and Quotients which are Newforms</a>
               .
%H A030209 W. Stein, <a href="http://modular.fas.harvard.edu:8080/mfd/space.html?space=[6,
               4,[]]&search=6">Modular Forms Database</a>.
%F A030209 Euler transform of period 6 sequence [ -2,-4,-4,-4,-2,-8,...]. - Michael 
               Somos Feb 13 2006
%F A030209 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
%F A030209 G.f.: x*(Product_{k>0} (1-x^k)(1-x^(2k))(1-x^(3k))(1-x^(6k)))^2.
%e A030209 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 +...
%o A030209 (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 */
%Y A030209 Sequence in context: A000793 A062163 A002729 this_sequence A138588 A143102 
               A013944
%Y A030209 Adjacent sequences: A030206 A030207 A030208 this_sequence A030210 A030211 
               A030212
%K A030209 sign,mult
%O A030209 1,2
%A A030209 N. J. A. Sloane (njas(AT)research.att.com).

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