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A279955
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Expansion of chi(-x^4)^4 * f(-x^4)^2 * f(-x)^2 in powers of x where chi(), f() are Ramanujan theta functions.
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5
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1, -2, -1, 2, -5, 14, 4, -12, 5, -40, 0, 26, 11, 68, -15, -30, -18, -106, 3, 50, -10, 182, 29, -104, 10, -270, 11, 130, 37, 360, -51, -164, -16, -506, -30, 266, -65, 686, 62, -320, 53, -898, 22, 414, 50, 1206, -61, -612, -52, -1560, -4, 696, -81, 1958, 120
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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
Amanda Clemm, Modular Forms and Weierstrass Mock Modular Forms, Mathematics, volume 4, issue 1, (2016)
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 * eta(q^4)^2 * eta(q^16)^6 / eta(q^32)^4 in powers of q^4.
Euler transform of period 8 sequence [ -2, -2, -2, -8, -2, -2, -2, -4, ...].
a(n) = (-1)^n * A280339(n).
a(3*n + 1) / a(1) == A002171(n) (mod 3). a(3^3*n + 7) / a(7) == A002171(n) (mod 3^2).
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EXAMPLE
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G.f. = 1 - 2*x - x^2 + 2*x^3 - 5*x^4 + 14*x^5 + 4*x^6 - 12*x^7 + 5*x^8 + ...
G.f. = q^-1 - 2*q^3 - q^7 + 2*q^11 - 5*q^15 + 14*q^19 + 4*q^23 - 12*q^27 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^4]^2 QPochhammer[ x^4, x^8]^4, {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)^2 * eta(x^4 + A)^6 / eta(x^8 + A)^4, n))};
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CROSSREFS
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Cf. A002171, A280339.
Sequence in context: A327194 A160457 A107087 * A280339 A115141 A031148
Adjacent sequences: A279952 A279953 A279954 * A279956 A279957 A279958
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Dec 23 2016
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STATUS
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approved
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