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A143161
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Expansion of q^(1/6) * eta(q)^2 / (eta(q^2) * eta(q^4)) in powers of q.
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0
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1, -2, 0, 0, 3, -2, 0, 0, 4, -6, 0, 0, 7, -8, 0, 0, 13, -14, 0, 0, 19, -20, 0, 0, 29, -34, 0, 0, 43, -46, 0, 0, 62, -70, 0, 0, 90, -96, 0, 0, 126, -138, 0, 0, 174, -186, 0, 0, 239, -262, 0, 0, 325, -346, 0, 0, 435, -472, 0, 0, 580, -620, 0, 0, 769, -826, 0, 0, 1007, -1072, 0, 0, 1313, -1408, 0, 0, 1702
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of chi(-q)^2 * chi(-q^2) in powers of q where chi() is a Ramanujan theta function.
Euler transform of period 4 sequence [ -2, -1, -2, 0, ...].
a(4*n + 2) = a(4*n + 3) = 0.
G.f.: (Product_{k>0} (1 + x^k)^2 * (1 + x^(2*k)))^-1.
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EXAMPLE
| 1/q - 2*q^5 + 3*q^23 - 2*q^29 + 4*q^47 - 6*q^53 + 7*q^71 - 8*q^77 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 / eta(x^2 + A) / eta(x^4 + A), n))}
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CROSSREFS
| A029552(n) = a(4*n). -2 * A098613(n) = a(4*n + 1).
Sequence in context: A174169 A113411 A125095 * A142886 A099026 A205341
Adjacent sequences: A143158 A143159 A143160 * A143162 A143163 A143164
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Jul 27 2008
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