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Search: id:A128512
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| A128512 |
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Expansion of q^(-1)* (chi(-q)* chi(-q^9)/ chi(-q^3)^2)^6 in powers of q where chi() is a Ramanujan theta function. |
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+0
1
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| 1, -6, 15, -14, -21, 78, -62, -132, 399, -322, -426, 1332, -964, -1524, 4278, -3072, -4059, 11454, -7802, -11148, 29892, -20284, -26268, 70488, -46341, -62484, 162537, -106340, -135291, 351120, -224958, -292536, 743862, -474370, -594180, 1506060, -946310
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of ((c(q^2)^2* b(q^3)* c(q^3))/ (c(q)^2* b(q^6)* c(q^6)))^3 in powers of q where b(),c() are cubic AGM functions.
Expansion of ((eta(q)* eta(q^9)* eta(q^6)^2)/ (eta(q^2)* eta(q^18)* eta(q^3)^2))^6 in powers of q.
Euler transform of period 18 sequence [ -6, 0, 6, 0, -6, 0, -6, 0, 0, 0, -6, 0, -6, 0, 6, 0, -6, 0, ...].
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* (12*(1+v^2) +172*v).
G.f.: (1/x)* (Product_{k>0} (1 -x^k +x^(2k))/(1 -x^(3k) +x(6k)))^6.
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EXAMPLE
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1/q - 6 + 15*q - 14*q^2 - 21*q^3 + 78*q^4 - 62*q^5 - 132*q^6 + ...
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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+A)* eta(x^9+A)* et a(x^6+A)^2/ eta(x^2+A)/ eta(x^18+A)/ eta(x^3+A)^2)^6, n))}
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CROSSREFS
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Sequence in context: A070870 A123623 A070555 this_sequence A009579 A114812 A139204
Adjacent sequences: A128509 A128510 A128511 this_sequence A128513 A128514 A128515
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 05 2007
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