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Search: id:A161970
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| A161970 |
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Expansion of eta(q) * eta(q^7) / (eta(q^4) * eta(q^28)) in powers of q. |
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+0
1
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| 1, -1, -1, 0, 1, 0, -1, 0, 3, 0, -2, 0, 2, 0, -5, 0, 6, 0, -7, 0, 7, 0, -9, 0, 12, 0, -13, 0, 16, 0, -20, 0, 25, 0, -27, 0, 31, 0, -38, 0, 44, 0, -51, 0, 58, 0, -69, 0, 80, 0, -92, 0, 102, 0, -118, 0, 141, 0, -157, 0, 177, 0, -203, 0, 234, 0, -261, 0, 292, 0, -336, 0, 382, 0, -428, 0, 475, 0, -540, 0, 610
(list; graph; listen)
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OFFSET
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-1,9
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FORMULA
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Expansion of chi(-q) * chi(-q^2) * chi(-q^7) * chi(-q^14) in power of q where chi() is a Ramanaujan theta function.
Euler transform of period 28 sequence [ -1, -1, -1, 0, -1, -1, -2, 0, -1, -1, -1, 0, -1, -2, -1, 0, -1, -1, -1, 0, -2, -1, -1, 0, -1, -1, -1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u * (u + 2) * (v + 2) - v^2.
G.f. is a period 1 Fourier series which satisfies f(-1 / (28 t)) = 4 / f(t) where q = exp(2 pi i t).
a(2*n) = 0 unless n = 0.
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EXAMPLE
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1/q - 1 - q + q^3 - q^5 + 3*q^7 - 2*q^9 + 2*q^11 - 5*q^13 + 6*q^15 + ...
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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^7 + A) / (eta(x^4 + A) * eta(x^28 + A)) , n))}
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CROSSREFS
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Sequence in context: A011339 A166243 A118514 this_sequence A059339 A092735 A035464
Adjacent sequences: A161967 A161968 A161969 this_sequence A161971 A161972 A161973
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 22 2009
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