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Search: id:A138270
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| A138270 |
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Expansion of phi(-q^3) * phi(-q^4) in powers of q where phi() is a Ramanujan theta function. |
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+0
2
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| 1, 0, 0, -2, -2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Euler transform of period 24 sequence [ 0, 0, -2, -2, 0, -1, 0, -1, -2, 0, 0, -3, 0, 0, -2, -1, 0, -1, 0, -2, -2, 0, 0, -2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 192^(1/2) (t/i) g(t) where q = exp(2 pi i t) and g() is g.f. for A112609.
a(3*n+2) = a(4*n+1) = a(4*n+2) = 0.
Expansion of (eta(q^3) * eta(q^4))^2 / (eta(q^6) * eta(q^8)) in powers of q.
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EXAMPLE
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1 - 2*q^3 - 2*q^4 + 4*q^7 + 2*q^12 - 2*q^16 - 4*q^19 - 2*q^27 + 4*q^28 + ...
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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^3 + A) * eta(x^4 + A))^2 / (eta(x^6 + A) * eta(x^8 + A)), n))}
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CROSSREFS
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Sequence in context: A014473 A101164 A062275 this_sequence A134315 A119332 A089262
Adjacent sequences: A138267 A138268 A138269 this_sequence A138271 A138272 A138273
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 10 2008, Apr 04 2008
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