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A215600
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Expansion of psi(-x)^2 * f(-x)^6 in powers of x where psi(), f() are Ramanujan theta functions.
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4
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1, -8, 22, -16, -27, 40, -18, 80, -94, -40, 0, -48, 359, -80, -130, -320, 0, 160, 214, 400, -230, -152, -594, 416, -343, 240, 518, -400, 0, 200, 830, -592, -396, -776, 0, -400, 1098, 200, 0, 1120, 729, -552, -2068, 272, -1670, 800, 0, 400, 594, 1480, 598, 48
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of psi(-x)^8 * chi(-x^2)^6 = f(-x)^8 / chi(-x^2)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions. - Michael Somos, Sep 03 2013
Expansion of q^(-1/2) * (eta(q)^4 * eta(q^4) / eta(q^2))^2 in powers of q.
Euler transform of period 4 sequence [ -8, -6, -8, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 2^15 (t/i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A225564. - Michael Somos, Sep 03 2013
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EXAMPLE
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1 - 8*x + 22*x^2 - 16*x^3 - 27*x^4 + 40*x^5 - 18*x^6 + 80*x^7 - 94*x^8 + ...
q - 8*q^3 + 22*q^5 - 16*q^7 - 27*q^9 + 40*q^11 - 18*q^13 + 80*q^15 - 94*q^17 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ q]^6 EllipticTheta[ 2, Pi/4, q^(1/2)]^2 / (2 q^(1/4)), {q, 0, n}] (* Michael Somos, Sep 03 2013 *)
a[ n_] := SeriesCoefficient[ QPochhammer[ q]^8 / QPochhammer[ q^2, q^4]^2, {q, 0, n}] (* Michael Somos, Sep 03 2013 *)
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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 + A)^4 * eta(x^4 + A) / eta(x^2 + A))^2, n))}
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CROSSREFS
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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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