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A137566
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Expansion of q^(1/6) * eta(q) / ( eta(q^2) * eta(q^3) ) in powers of q.
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1
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1, -1, 0, 0, 0, -1, 2, -2, 1, 0, 0, -2, 5, -5, 2, 0, 1, -5, 10, -10, 5, -1, 2, -10, 20, -20, 10, -2, 5, -20, 36, -36, 20, -6, 10, -36, 65, -65, 36, -12, 21, -65, 110, -110, 65, -25, 38, -110, 185, -185, 110, -46, 70, -185, 300, -300, 186, -85, 120, -300, 481, -481, 302, -146, 205, -482, 752, -752, 486, -250
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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FORMULA
| Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, 1, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (864 t)) = 24^(-1/2) (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A007690.
G.f.: (Product_{k>0} (1 + x^k) * (1 - x^(3*k)))^(-1).
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EXAMPLE
| q^-1 - q^5 - q^29 + 2*q^35 - 2*q^41 + q^47 - 2*q^65 + 5*q^71 + ...
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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^2 + A) / eta(x^3 + A), n))}
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CROSSREFS
| Sequence in context: A181169 A029390 A108040 * A122865 A074080 A179769
Adjacent sequences: A137563 A137564 A137565 * A137567 A137568 A137569
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Jan 26 2008
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