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A133078
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Expansion of b(q)^4 in powers of q where b() is a cubic AGM function.
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0
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1, -12, 54, -84, -147, 756, -756, -1212, 3510, -2028, -3402, 7992, -6132, -5964, 18576, -10584, -14619, 29484, -18252, -21084, 55188, -28896, -35964, 73008, -49140, -46128, 118692, -54516, -73896, 146340, -95256, -92148, 224694, -111888, -132678, 260064, -148044
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| Expansion of ( eta(q)^3 / eta(q^3) )^4 in powers of q.
Euler transform of period 3 sequence [ -12, -12, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (3 t)) = 729 (t/i)^4 g(t) where q = exp(2 pi i t) and g(t) is g.f. for A033690.
G.f.: ( Product_{k>0} (1 - x^k)^3 / (1 - x^(3*k)) )^4.
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EXAMPLE
| 1 - 12*q + 54*q^2 - 84*q^3 - 147*q^4 + 756*q^5 - 756*q^6 - 1212*q^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x*O(x^n); polcoeff( ( eta(x + A)^3 / eta(x^3 + A) )^4, n))}
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CROSSREFS
| Sequence in context: A195544 A030182 A060171 * A034436 A186210 A000735
Adjacent sequences: A133075 A133076 A133077 * A133079 A133080 A133081
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Sep 08 2007
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