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A132322
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Expansion of q^-1 * chi(-q) * chi(-q^23) in powers of q where chi() is a Ramanujan theta function.
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0
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1, -1, 0, -1, 1, -1, 1, -1, 2, -2, 2, -2, 3, -3, 3, -4, 5, -5, 5, -6, 7, -8, 8, -10, 12, -12, 13, -15, 17, -18, 19, -22, 25, -27, 28, -32, 36, -38, 41, -46, 51, -54, 58, -64, 71, -76, 81, -89, 99, -105, 112, -123, 134, -143, 153, -167, 182, -194, 207, -225, 244, -260, 277, -301, 325, -346, 369, -398, 429, -458
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,9
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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
| Expansion of eta(q) * eta(q^23) / (eta(q^2) * eta(q^46)) in powers of q.
Euler transform of period 46 sequence [ -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -2, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * v - v^2 + 2 * u + 2 * u * v.
G.f. is a Fourier series which satisfies f(-1 / (46 t)) = 2 / f(t) where q = exp(2 pi i t).
G.f.: x^-1 * (Product_{k>0} (1+x^k) * (1+x^(23*k)))^-1.
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EXAMPLE
| 1/q - 1 - q^2 + q^3 - q^4 + q^5 - q^6 + 2*q^7 - 2*q^8 + 2*q^9 - 2*q^10 + ...
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PROG
| (PARI) {a(n) = local(A); if(n<-1, 0, n++; A = x*O(x^n); polcoeff( eta(x+A) * eta(x^23+A) / eta(x^2+A) / eta(x^46+A), n))}
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CROSSREFS
| A058688(n) = a(n) unless n = 0.
Sequence in context: A081362 A112216 A058688 * A018118 A029084 A032229
Adjacent sequences: A132319 A132320 A132321 * A132323 A132324 A132325
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 18 2007
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