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A139135
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Expansion of psi(-q^3) / f(q) where psi(), f() are Ramanujan theta functions.
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3
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1, -1, 2, -4, 6, -9, 14, -20, 29, -42, 58, -80, 110, -148, 198, -264, 347, -454, 592, -764, 982, -1257, 1598, -2024, 2554, -3206, 4010, -5000, 6208, -7684, 9484, -11664, 14306, -17501, 21346, -25972, 31526, -38170, 46112, -55588, 66861, -80258, 96154, -114968, 137212
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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^(-1/3) * eta(q) * eta(q^3) * eta(q^4) * eta(q^12) / (eta(q^2)^3 * eta(q^6)) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (108 t)) = 3^(-1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139136.
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EXAMPLE
| q - q^4 + 2*q^7 - 4*q^10 + 6*q^13 - 9*q^16 + 14*q^19 - 20*q^22 + 29*q^25 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / (eta(x^2 + A)^3 * eta(x^6 + A)), n))}
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CROSSREFS
| A139136(3*n + 1) = - a(n). A139137(3*n + 1) = 2 * a(n).
Apart from signs, same as A097197.
Sequence in context: A034748 A069916 A153140 * A097197 A119737 A038718
Adjacent sequences: A139132 A139133 A139134 * A139136 A139137 A139138
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Apr 10 2008
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