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A139631
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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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3
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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
(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^10)^2 / (eta(q^2) * eta(q^5) * eta(q^20)) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (640 t)) = 2^(-1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139632.
G.f.: Product_{k>0} (1 + x^(2*k)) * (1 + x^(5*k)) / (1 + x^(10*k)).
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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^10 + A)^2 / eta(x^2 + A) / eta(x^5 + A) / eta(x^20 + A), n))}
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CROSSREFS
| A139632(2*n) = a(n).
Sequence in context: A154958 A025806 A025802 * A145706 A029177 A161229
Adjacent sequences: A139628 A139629 A139630 * A139632 A139633 A139634
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 27 2008
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