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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| 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
| 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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PROG
| (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
| Sequence in context: A014473 A101164 A062275 * A179011 A134315 A119332
Adjacent sequences: A138267 A138268 A138269 * A138271 A138272 A138273
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Mar 10 2008, Apr 04 2008
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