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Search: id:A112128
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| A112128 |
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Expansion of (eta(q)/eta(q^16))^2(eta(q^8)/eta(q^2))^5 in powers of q. |
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+0
1
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| 1, -2, 4, -8, 16, -28, 48, -80, 128, -202, 312, -472, 704, -1036, 1504, -2160, 3072, -4324, 6036, -8360, 11488, -15680, 21264, -28656, 38400, -51182, 67864, -89552, 117632, -153836, 200352, -259904, 335872, -432480, 554952, -709728, 904784, -1149916, 1457136
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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C. Adiga and N. Anitha, A note on a continued fraction of Ramanujan, Bull. Austral. Math. Soc. 70 (2004), pp. 489-497. MR2103981 (2005g:11009)
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FORMULA
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Euler transform of period 16 sequence [ -2, 3, -2, 3, -2, 3, -2, -2, -2, 3, -2, 3, -2, 3, -2, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=u^2-(1-2u+2u^2)(1-2v+2v^2).
G.f.: (Sum_k x^(4k^2))/(Sum_k x^(k^2)) = theta_3(x^4)/theta_3(x).
G.f.: Product_{k>0} ((1+x^(2k))(1+x^(4k)))^3/((1+x^k)(1+x^(8k)))^2.
Expansion of continued fraction 1/(1+2*x/(1-x^2+(x^1+x^3)^2/(1-x^6+(x^2+x^6)^2/(1-x^10+(x^3+x^9)^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)^2*eta(x^8+A)^5/eta(x^2+A)^5/eta(x^16+A)^2, n))}
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CROSSREFS
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Sequence in context: A104899 A057975 A089055 this_sequence A054189 A127195 A018726
Adjacent sequences: A112125 A112126 A112127 this_sequence A112129 A112130 A112131
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 27 2005
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