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Search: id:A121665
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| A121665 |
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Expansion of (eta(q^2)* eta(q^3)/ (eta(q)* eta(q^6)))^12 in powers of q. |
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| 1, 12, 78, 364, 1365, 4380, 12520, 32772, 80094, 185276, 409578, 871272, 1792754, 3582708, 6977100, 13277472, 24747867, 45267324, 81389908, 144048396, 251265288, 432425864, 734953116, 1234647216, 2051576037, 3374318100
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OFFSET
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-1,2
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FORMULA
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Expansion of (1/q)(chi(-q^3)/chi(-q))^12 in powers of q where chi() is a Ramanujan theta function.
Euler transform of period 6 sequence [ 12, 0, 0, 0, 12, 0, ...].
G.f.: 1/x(Product_{k>0} (1-x^k+x^(2k)))^-12.
Expansion of ((c(q)*b(q^2))/(c(q^2)*b(q)))^3 in powers of q where b(),c() are cubic AGM analog functions.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)= (u^2-v)* (w^2-v) -u*w* (24*(1+v^2) +152*v).
G.f. is Fourier series of a level 6 modular function. f(-1/(6t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
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1/q +12 +78*q +364*q^2 +1365*q^3 +4380*q^4 +12520*q^5 +...
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PROGRAM
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(PARI) {a(n)= if(n<-1, 0, n++; A=x*O(x^n); polcoeff( (eta(x^2+A)* eta(x^3+A)/ eta(x+A)/ eta(x^6+A))^12, n))}
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CROSSREFS
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Cf. A007255, A045485.
Sequence in context: A008504 A008494 A001288 this_sequence A124863 A022577 A030116
Adjacent sequences: A121662 A121663 A121664 this_sequence A121666 A121667 A121668
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 14 2006
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