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A139632
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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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3
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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
(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^2)^2 * eta(q^5) / (eta(q) * eta(q^4) * eta(q^10)) 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 A139631.
G.f.: Product_{k>0} (1 + x^k) / ((1 + x^(2*k)) * (1 + x^(5*k))).
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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^2 + A)^2 * eta(x^5 + A) / eta(x + A) / eta(x^4 + A) / eta(x^10 + A), n))}
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CROSSREFS
| A139631(n) = a(2*n).
Sequence in context: A117957 * A145704 A145705 A145702 A029339 A029364
Adjacent sequences: A139629 A139630 A139631 * A139633 A139634 A139635
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 27 2008
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