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A145706
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Expansion of chi(-q^5) / chi(-q^2) in powers of q where chi() is a Ramanujan theta function.
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2
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1, 0, 1, 0, 1, -1, 2, -1, 2, -1, 3, -2, 4, -2, 5, -4, 6, -5, 8, -6, 11, -8, 13, -10, 16, -14, 20, -17, 24, -21, 31, -26, 37, -32, 44, -41, 54, -49, 64, -59, 79, -72, 94, -86, 111, -106, 132, -126, 156, -149, 187, -178, 219, -210, 257, -251, 302, -295, 352, -346, 416, -406, 483, -474, 560, -558, 652, -648, 754, -752
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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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 q^(1/8) * eta(q^4) * eta(q^5) / (eta(q^2) * eta(q^10)) in powers of q.
Euler transform of period 20 sequence [ 0, 1, 0, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (1280 t)) = f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 - x^(10*k - 5)) / (1 - x^(4*k - 2)).
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EXAMPLE
| 1/q + q^15 + q^31 - q^39 + 2*q^47 - q^55 + 2*q^63 - q^71 + 3*q^79 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^5 + A) / (eta(x^2 + A) * eta(x^10 + A)), n))}
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CROSSREFS
| (-1)^n * A139631(n) = A145704(2*n) = A145705(2*n) = a(n).
Sequence in context: A025806 A025802 A139631 * A029177 A161229 A029176
Adjacent sequences: A145703 A145704 A145705 * A145707 A145708 A145709
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 17 2008, Oct 20 2008
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