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Search: id:A131946
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| A131946 |
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Expansion of (eta(q) * eta(q^3))^4/( eta(q^2) * eta(q^6))^2 in powers of q. |
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+0
2
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| 1, -4, 4, -4, 20, -24, 4, -32, 52, -4, 24, -48, 20, -56, 32, -24, 116, -72, 4, -80, 120, -32, 48, -96, 52, -124, 56, -4, 160, -120, 24, -128, 244, -48, 72, -192, 20, -152, 80, -56, 312, -168, 32, -176, 240, -24, 96, -192, 116, -228, 124, -72, 280, -216, 4, -288, 416, -80, 120, -240, 120, -248, 128, -32
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 85, Eq. (32.66).
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FORMULA
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Expansion of (phi(-q)* phi(-q^3))^2 in powers of q where phi() is a Ramanujan theta function.
Expansion of (4*a(q^2)^2 -a(q)^2)/3 = (b(q)^2/b(q^2))* (c(q)^2/c(q^2))/3 in powers of q where a(),b(),c() are cubic AGM function.
Euler transform of period 6 sequence [ -4, -2, -8, -2, -4, -4, ...].
G.f.: 1 -4*( Sum_{k>0} k* (-x)^k/(1-x^k)* kronecker(9, k)) = (theta_3(-x)* theta_3(-x^3))^2.
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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+A)* eta(x^3+A))^4/( eta(x^2+A)* eta(x^6+A))^2, n))}
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CROSSREFS
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(-1)^n*A034896(n) = a(n). -4*A131947(n) = a(n) unless n = 0.
Sequence in context: A098525 A141666 A102127 this_sequence A034896 A120914 A024949
Adjacent sequences: A131943 A131944 A131945 this_sequence A131947 A131948 A131949
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jul 30 2007
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