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Search: id:A121666
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| A121666 |
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Expansion of (eta(q)eta(q^3)/(eta(q^2)eta(q^6)))^6 in powers of q. |
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+0
1
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| 1, -6, 15, -32, 87, -192, 343, -672, 1290, -2176, 3705, -6336, 10214, -16320, 25905, -39936, 61227, -92928, 138160, -204576, 300756, -435328, 626727, -897408, 1271205, -1790592, 2508783, -3487424, 4824825, -6641664, 9083400, -12371904, 16778784, -22630912
(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 (1/q)(chi(-q^3)chi(-q))^6 in powers of q where chi() is a Ramanujan theta function.
Euler transform of period 6 sequence [ -6, 0, -12, 0, -6, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u,v)=v*u^2+(12*v+64)*u-v^2
G.f.: 1/x(Product_{k>0} (1+x^k)(1+x^(3k)))^-6.
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EXAMPLE
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1/q -6 +15*q -32*q^2 +87*q^3 -192*q^4 +343*q^5 -672*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^3+A)/eta(x^2+A)/eta(x^6+A))^6, n))}
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CROSSREFS
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Cf. A007256, A045486.
Sequence in context: A092411 A134506 A143274 this_sequence A118734 A051410 A083052
Adjacent sequences: A121663 A121664 A121665 this_sequence A121667 A121668 A121669
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 14 2006
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