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Search: id:A137830
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| A137830 |
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Expansion of phi(-q) / f(-q^4)^2 in powers of q where phi(), f() are Ramanujan theta functions. |
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2
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| 1, -2, 0, 0, 4, -4, 0, 0, 9, -12, 0, 0, 20, -24, 0, 0, 42, -50, 0, 0, 80, -92, 0, 0, 147, -172, 0, 0, 260, -296, 0, 0, 445, -510, 0, 0, 744, -840, 0, 0, 1215, -1372, 0, 0, 1944, -2176, 0, 0, 3059, -3424, 0, 0, 4740, -5268, 0, 0, 7239, -8040, 0, 0, 10920, -12072, 0, 0, 16286, -17976, 0, 0, 24028
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of q^(1/3) * eta(q)^2 / (eta(q^2) * eta(q^4)^2) in powers of q.
Euler transform of period 4 sequence [ -2, -1, -2, 1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = (4/3)^(1/2) (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A137829.
a(4*n+2) = a(4*n+3) = 0.
G.f.: ( Product_{k>0} (1 - x^(2*k)) * (1 + x^k)^2 * (1 + x^(2*k))^2 )^(-1).
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EXAMPLE
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1/q - 2*q^2 + 4*q^11 - 4*q^14 + 9*q^23 - 12*q^26 + 20*q^35 - 24*q^38 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 / eta(x^2 + A) / eta(x^4 + A)^2, n))}
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CROSSREFS
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Cf. A137828(n) = |a(n)|. A051136(n) = a(4*n). -2 * A137829(n) = a(4*n+1).
Sequence in context: A045836 A072070 A137828 this_sequence A137505 A107498 A094295
Adjacent sequences: A137827 A137828 A137829 this_sequence A137831 A137832 A137833
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 12 2008
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