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Search: id:A139135
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| A139135 |
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Expansion of psi(-q^3) / f(q) where psi(), f() are Ramanujan theta functions. |
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+0
4
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| 1, -1, 2, -4, 6, -9, 14, -20, 29, -42, 58, -80, 110, -148, 198, -264, 347, -454, 592, -764, 982, -1257, 1598, -2024, 2554, -3206, 4010, -5000, 6208, -7684, 9484, -11664, 14306, -17501, 21346, -25972, 31526, -38170, 46112, -55588, 66861, -80258, 96154, -114968, 137212
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Expansion of q^(-1/3) * eta(q) * eta(q^3) * eta(q^4) * eta(q^12) / (eta(q^2)^3 * eta(q^6)) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (108 t)) = 3^(-1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139136.
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EXAMPLE
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q - q^4 + 2*q^7 - 4*q^10 + 6*q^13 - 9*q^16 + 14*q^19 - 20*q^22 + 29*q^25 + ...
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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) * eta(x^4 + A) * eta(x^12 + A) / (eta(x^2 + A)^3 * eta(x^6 + A)), n))}
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CROSSREFS
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A139136(3*n + 1) = - a(n). A139137(3*n + 1) = 2 * a(n).
Apart from signs, same as A097197.
Adjacent sequences: A139132 A139133 A139134 this_sequence A139136 A139137 A139138
Sequence in context: A003402 A034748 A069916 this_sequence A097197 A119737 A038718
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 10 2008
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