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A134078
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Expansion of (phi(-q) / phi(-q^2))^3 * phi(q^3)^5 / phi(-q^6) in powers of q where phi() is a Ramanujan theta function.
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2
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1, -6, 18, -34, 42, -36, 30, -48, 90, -118, 108, -72, 54, -84, 144, -204, 186, -108, 66, -120, 252, -272, 216, -144, 102, -186, 252, -370, 336, -180, 180, -192, 378, -408, 324, -288, 90, -228, 360, -476, 540, -252, 240, -264, 504, -708, 432, -288, 198, -342, 558, -612, 588, -324, 174, -432, 720, -680, 540, -360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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 12 sequence [ -6, 3, 4, 0, -6, -10, -6, 0, 4, 3, -6, -4, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 8 (t/i)^2 g(t) where q = exp(2 pi i t) and g() is g.f. for A133739.
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EXAMPLE
| 1 - 6*q + 18*q^2 - 34*q^3 + 42*q^4 - 36*q^5 + 30*q^6 - 48*q^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^6 * eta(x^4 + A)^3 * eta(x^6 + A)^23 / ( eta(x^2 + A)^9 * eta(x^3 + A)^10 * eta(x^12 + A)^9 ), n))}
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CROSSREFS
| -36 * A098098(n) = a(6*n+5). 18 * A134079(n) = a(3*n+2).
Sequence in context: A124353 A153126 A110671 * A181510 A038343 A110965
Adjacent sequences: A134075 A134076 A134077 * A134079 A134080 A134081
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 06 2007
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