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Search: id:A135763
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| A135763 |
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Expansion of (theta_3(q) * theta_3(q^3))^3 in powers of q. |
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1
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| 1, 6, 12, 14, 42, 96, 84, 108, 300, 278, 144, 480, 546, 252, 600, 672, 618, 1152, 732, 828, 2016, 1276, 720, 2112, 2100, 1302, 2040, 2078, 2100, 3360, 1872, 1740, 4908, 3360, 1728, 4800, 5082, 2844, 4344, 4684, 3600, 6720, 4200, 3612, 10080, 5856
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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FORMULA
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Expansion of (phi(q) * phi(q^3))^3 in powers of q where phi() is a Ramanujan theta function.
Euler transform of period 12 sequence [ 6, -9, 12, -3, 6, -18, 6, -3, 12, -9, 6, -6, ...].
G.f. is a weight 3 level 12 modular form. f(-1/ (12 t)) = 1728^(1/2) (t/I)^3 f(t) where q = exp(2 pi i t).
G.f.: ( ( Sum_{k} x^(k^2) ) * ( Sum_{k} x^(3*k^2) ) )^3.
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EXAMPLE
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1 + 6*q + 12*q^2 + 14*q^3 + 42*q^4 + 96*q^5 + 84*q^6 + 108*q^7 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^6 + A))^15 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A))^6, n))}
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CROSSREFS
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Sequence in context: A079946 A118586 A113791 this_sequence A030659 A114304 A107487
Adjacent sequences: A135760 A135761 A135762 this_sequence A135764 A135765 A135766
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Nov 28 2007
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