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Search: id:A132107
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| A132107 |
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Expansion of (f(q)/ f(q^3))^6 in powers of q where f() is a Ramanujan theta function. |
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1
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| 1, 6, 9, -16, -66, -54, 98, 300, 243, -364, -1128, -828, 1221, 3498, 2511, -3528, -9876, -6804, 9358, 25428, 17217, -23068, -61644, -40824, 53916, 141318, 92340, -119912, -310554, -199980, 256792, 656436, 418311, -530960, -1344144, -847584, 1066157, 2673372
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Euler transform of period 12 sequence [ 6, -12, 0, -6, 6, 0, 6, -6, 0, -12, 6, 0, ...].
G.f. is a Fourier series which satisfies f(-1/(12 t)) = 27/ f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1+x^k)* (1-x^(2*k))* (1+x^(3*k))* (1-x^(6*k))/( (1+x^(2*k))* (1+x^(6*k))))^6.
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EXAMPLE
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1/q + 6*q + 9*q^3 - 16*q^5 - 66*q^7 - 54*q^9 + 98*q^11 + 300*q^13 + ...
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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)^3* eta(x^3+A)* eta(x^12+A)/ ( eta(x+A) *eta(x^4+A)* eta(x^6+A)^3))^6, n))}
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CROSSREFS
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Adjacent sequences: A132104 A132105 A132106 this_sequence A132108 A132109 A132110
Sequence in context: A031209 A031326 A007262 this_sequence A129317 A020183 A039280
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 09 2007
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