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Search: id:A095123
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| A095123 |
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Expansion of ((eta(q)eta(q^15))/(eta(q^3)eta(q^5)))^3 in powers of q. |
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+0
1
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| 1, -3, 0, 8, -9, 3, 8, -27, 24, 19, -48, 24, 17, -54, 57, 46, -147, 51, 145, -222, 123, 160, -459, 315, 306, -678, 360, 326, -870, 633, 612, -1581, 723, 1286, -2301, 1242, 1522, -3864, 2451, 2455, -5478, 2934, 2924, -7044, 4599, 4622, -11271, 5514, 8133, -15591, 8508
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^3+v^3+uv(-1+6(u+v)-uv).
Euler transform of period 15 sequence [ -3,-3,0,-3,0,0,-3,-3,0,0,-3,0,-3,-3,0,...].
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REFERENCES
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B. C. Berndt, H. H. Chan, S.-S. Huang, Incomplete Elliptic Integrals in Ramanujan's Lost Notebook, in q-series from a Contemporary Perspective, M. E. H. Ismail and D. Stanton, eds., Amer. Math. Soc., 2000, pp. 79-126.
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LINKS
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B. C. Berndt, H. H. Chan, S.-S. Huang, Incomplete Elliptic Integrals in Ramanujan's Lost Notebook.
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FORMULA
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G.f. x(Prod_{k>0} ((1-x^k)(1-x^(15k)))/(1-x^(3k))(1-x^(5k)))^3.
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PROGRAM
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(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff((eta(x+A)*eta(x^15+A)/eta(x^3+A)/eta(x^5+A))^3, n))
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CROSSREFS
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Sequence in context: A068458 A011082 A021768 this_sequence A019691 A068607 A134975
Adjacent sequences: A095120 A095121 A095122 this_sequence A095124 A095125 A095126
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KEYWORD
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sign
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AUTHOR
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Michael Somos, May 28 2004
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