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Search: id:A135211
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| A135211 |
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Expansion of q^(1/4) * eta(q) * eta(q^4) * eta(q^6) / ( eta(q^2) * eta(q^3) * eta(q^12) ) in powers of q. |
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1
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| 1, -1, 0, 0, -1, 0, 1, -1, 0, 2, -1, 0, 2, -2, 0, 2, -3, 0, 3, -3, 0, 4, -4, 0, 5, -6, 0, 6, -7, 0, 7, -8, 0, 10, -10, 0, 13, -13, 0, 14, -16, 0, 17, -18, 0, 22, -22, 0, 26, -28, 0, 30, -33, 0, 36, -38, 0, 44, -45, 0, 52, -55, 0, 60, -65, 0, 70, -74, 0, 84, -87, 0, 99, -104, 0, 112, -121, 0, 131, -138, 0, 156, -160
(list; graph; listen)
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OFFSET
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0,10
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FORMULA
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Expansion of psi(-q) / psi(-q^3) in powers of q where psi() is a Ramanujan theta function.
Euler transform of period 12 sequence [ -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, ...].
Given g.f. A(x), then B(x) = A(x^4) / x satisfies 0 = f(B(x), B(x^3)) where f(u, v) = (1 + v^4) - (1 + u*v)^3.
G.f. is a period 1 Fourier series which satisfies f(-1 / (192 t)) = sqrt(3) / f(t) where q = exp(2 pi i t).
a(3*n+2) = 0.
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EXAMPLE
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1/q - q^3 - q^15 + q^23 - q^27 + 2*q^35 - q^39 + 2*q^47 - 2*q^51 + ...
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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) * eta(x^4 + A) * eta(x^6 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))}
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CROSSREFS
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-A036018(n) = a(3*n+1). Convolution inverse of A036018.
Sequence in context: A146973 A003263 A157242 this_sequence A029294 A065434 A045832
Adjacent sequences: A135208 A135209 A135210 this_sequence A135212 A135213 A135214
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 22 2007, Nov 23 2007
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