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A233034
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Expansion of (f(-x^2) / phi(-x^3))^2 in powers of x where phi(), f() are Ramanujan theta functions.
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3
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1, 0, -2, 4, -1, -8, 14, -4, -23, 40, -10, -60, 98, -24, -140, 224, -54, -304, 478, -112, -627, 968, -224, -1236, 1884, -432, -2346, 3540, -801, -4320, 6454, -1448, -7742, 11472, -2556, -13548, 19936, -4408, -23226, 33952, -7462, -39080, 56800, -12416, -64660
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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Expansion of q^(-2/3) * b(q^2) * c(q^2) / (3 * f(-q^3)^4) in powers of q where b(), c() are cubic AGM theta functions.
Expansion of q^(-1/6) * (eta(q^2) * eta(q^6) / eta(q^3)^2)^2 in powers of q.
Euler transform of period 6 sequence [ 0, -2, 4, -2, 0, 0, ...].
G.f.: Product_{k>0} ( (1 - x^(2*k)) * (1 - x^(6*k)) / (1 - x^(3*k))^2 )^2.
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EXAMPLE
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G.f. = 1 - 2*x^2 + 4*x^3 - x^4 - 8*x^5 + 14*x^6 - 4*x^7 - 23*x^8 + 40*x^9 + ...
G.f. = q - 2*q^13 + 4*q^19 - q^25 - 8*q^31 + 14*q^37 - 4*q^43 - 23*q^49 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2] QPochhammer[ x^6] / QPochhammer[ x^3]^2)^2, {x, 0, n}];
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^6 + A) / eta(x^3 + A)^2)^2, n))};
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CROSSREFS
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Cf. A058531, A062242, A062244, A092848, A093073, A128111, A128143, A128144, A128145, A132976, A139032, A143840, A164268, A164612, A164615, A182032, A182033, A182034, A182035, A182056, A182057, A193261.
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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