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A260168
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Expansion of f(-x)^6 * f(-x^3)^2 / phi(-x^3)^8 in powers of q where phi(), f() are Ramanujan theta functions.
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1
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1, -6, 9, 24, -114, 126, 262, -1044, 999, 1852, -6672, 5868, 10103, -34134, 28341, 46336, -149400, 118872, 186926, -581412, 447507, 682340, -2062332, 1545336, 2297737, -6782508, 4970241, 7236280, -20938728, 15056694, 21531158, -61246128, 43329078, 61003980
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OFFSET
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0,2
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COMMENTS
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Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
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Expansion of q^(-1/2) * (eta(q)^3 * eta(q^6)^4 / eta(q^3)^7)^2 in powers of q.
Euler transform of period 6 sequence [ -6, -6, 8, -6, -6, 0, ...].
-2 * a(n) = A261576(2*n + 1).
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EXAMPLE
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G.f. = 1 - 6*x + 9*x^2 + 24*x^3 - 114*x^4 + 126*x^5 + 262*x^6 - 1044*x^7 + ...
G.f. = q - 6*q^3 + 9*q^5 + 24*q^7 - 114*q^9 + 126*q^11 + 262*q^13 - 1044*q^15 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x]^6 QPochhammer[ x^3]^2 / EllipticTheta[ 4, 0, x^3]^8, {x, 0, n}];
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 * eta(x^6 + A)^4 / eta(x^3 + A)^7)^2, n))};
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CROSSREFS
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Cf. A261576.
Sequence in context: A084431 A176498 A142877 * A093153 A115646 A260565
Adjacent sequences: A260165 A260166 A260167 * A260169 A260170 A260171
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Nov 09 2015
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STATUS
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approved
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