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Search: id:A164272
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| A164272 |
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Expansion of phi(q) * phi(-q^3) in powers of q where phi() is a Ramanujan theta function. |
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3
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| 1, 2, 0, -2, -2, 0, 0, -4, 0, 2, 0, 0, -2, 4, 0, 0, 6, 0, 0, -4, 0, 4, 0, 0, 0, 2, 0, -2, -4, 0, 0, -4, 0, 0, 0, 0, -2, 4, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 6, 6, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, -4, 6, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, -2, -4, 0, 0, -4, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, -8, 0, 4, 0, 0, 0, 4, 0, 0, -2, 0, 0, -4, 0
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of eta(q^2)^5 * eta(q^3)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 2, -3, 0, -1, 2, -4, 2, -1, 0, -3, 2, -2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (48 t)) = 768^(1/2) (t/i) g(t) where q = exp(2 pi i t) and g() is g.f. for A112604.
a(4*n + 2) = 0.
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EXAMPLE
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1 + 2*q - 2*q^3 - 2*q^4 - 4*q^7 + 2*q^9 - 2*q^12 + 4*q^13 + 6*q^16 + ...
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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^2 + A)^5 * eta(x^3 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A)), n))}
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CROSSREFS
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Cf. (-1)^n * A164273(n) = a(n). 2 * A129449(n) = a(2*n + 1). A115978(n) = a(4*n). 2 * A112604(n) = a(4*n + 1). -2 * A112605(n) = a(4*n + 3).
Sequence in context: A028928 A091379 A151758 this_sequence A164273 A106277 A088627
Adjacent sequences: A164269 A164270 A164271 this_sequence A164273 A164274 A164275
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 11 2009
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