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A145702
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Expansion of chi(-q) * chi(q^5) in powers of q where chi() is a Ramanujan theta function.
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1
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1, -1, 0, -1, 1, 0, 0, -1, 1, -1, 1, -1, 2, -1, 1, -1, 2, -2, 1, -2, 3, -3, 2, -3, 4, -3, 2, -4, 5, -4, 4, -5, 6, -6, 5, -6, 8, -7, 6, -8, 11, -10, 8, -11, 13, -11, 10, -13, 16, -15, 14, -17, 20, -18, 17, -20, 24, -23, 21, -25, 31, -29, 26, -32, 37, -34, 32, -39, 44, -42, 41, -47, 54, -52, 49, -56, 64, -62, 59, -68, 79, -77, 72, -83
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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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^(1/4) * eta(q) * eta(q^10)^2 / eta(q^2) / eta(q^5) / eta(q^20) in powers of q.
Euler transform of period 20 sequence [ -1, 0, -1, 0, 0, 0, -1, 0, -1, -1, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, ...].
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 A145703.
Product_{k>0} (1 - x^(2*k - 1)) * (1 + x^(10*k - 5)).
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EXAMPLE
| 1/q - q^3 - q^11 + q^15 - q^27 + q^31 - q^35 + q^39 - q^43 + 2*q^47 + ...
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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^10 + A)^2 / eta(x^2 + A) / eta(x^5 + A) / eta(x^20 + A), n))}
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CROSSREFS
| (-1)^n * A139632(n) = a(n). A139631(n) = a(2*n). - A145703(n) = a(2*n + 1).
Sequence in context: A139632 A145704 A145705 * A029339 A029364 A122586
Adjacent sequences: A145699 A145700 A145701 * A145703 A145704 A145705
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 17 2008
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