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A256637
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Expansion of psi(-q) * phi(-q^3)^2 / (q * psi(-q^3)^3) in powers of q where phi(), psi() are Ramanujan theta functions.
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1
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1, -1, 0, -2, 1, 0, 0, 2, 0, 2, 0, 0, 0, -4, 0, -4, -1, 0, 0, 6, 0, 8, 0, 0, 1, -10, 0, -12, 1, 0, 0, 16, 0, 18, 0, 0, -2, -24, 0, -28, -1, 0, 0, 36, 0, 40, 0, 0, 2, -52, 0, -58, 2, 0, 0, 74, 0, 84, 0, 0, -2, -104, 0, -116, -3, 0, 0, 144, 0, 160, 0, 0, 3
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OFFSET
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-1,4
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COMMENTS
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LINKS
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FORMULA
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Expansion of psi(-q) * f(q^3)^3 / (q * psi(q^3)^4) in powers of q where psi(), f() are Ramanujan theta functions.
Expansion of eta(q) * eta(q^3) * eta(q^4) * eta(q^6) / (eta(q^2) * eta(q^12)^3) in powers of q.
Euler transform of period 12 sequence [ -1, 0, -2, -1, -1, -2, -1, -1, -2, 0, -1, 0, ...].
a(3*n + 1) = a(4*n + 1) = 0. a(2*n) = - A139137(n). a(4*n - 1) = A256626(n).
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EXAMPLE
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G.f. = 1/q - 1 - 2*q^2 + q^3 + 2*q^6 + 2*q^8 - 4*q^12 - 4*q^14 - q^15 + ...
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MATHEMATICA
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eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[eta[q]* eta[q^3]*eta[q^4]*eta[q^6]/(eta[q^2]*eta[q^12]^3), {q, 0, n}]; Table[a[n], {n, -1, 100}] (* G. C. Greubel, Mar 14 2018 *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^6 + A) / (eta(x^2 + A) * eta(x^12 + A)^3), 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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