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A233670
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Expansion of q * phi(-q^2) * psi(q^9) / (f(q^3) * phi(q^3)) in powers of q where f(), phi(), psi() are Ramanujan theta functions.
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5
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1, 0, -2, -3, 0, 6, 8, 0, -14, -18, 0, 30, 38, 0, -60, -75, 0, 114, 140, 0, -208, -252, 0, 366, 439, 0, -626, -744, 0, 1044, 1232, 0, -1704, -1998, 0, 2730, 3182, 0, -4300, -4986, 0, 6672, 7700, 0, -10212, -11736, 0, 15438, 17673, 0, -23076, -26322, 0, 34134
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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Expansion of eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 * eta(q^18)^2 / (eta(q^4) * eta(q^6)^8 * eta(q^9)) in powers of q.
Euler transform of period 36 sequence [ 0, -2, -3, -1, 0, 3, 0, -1, -2, -2, 0, 1, 0, -2, -3, -1, 0, 2, 0, -1, -3, -2, 0, 1, 0, -2, -2, -1, 0, 3, 0, -1, -3, -2, 0, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 Pi i t).
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EXAMPLE
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G.f. = q - 2*q^3 - 3*q^4 + 6*q^6 + 8*q^7 - 14*q^9 - 18*q^10 + 30*q^12 + ...
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MATHEMATICA
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A233670[n_] := SeriesCoefficient[q*QPochhammer[q^2]^2*QPochhammer[q^3]^3 *QPochhammer[q^12]^3*QPochhammer[q^18]^2/(QPochhammer[q^4] * QPochhammer[q^6]^8*QPochhammer[q^9]), {q, 0, n}]; Table[A233670[n], {n, 50}] (* G. C. Greubel, Oct 09 2017 *)
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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^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 * eta(x^18 + A)^2 / (eta(x^4 + A) * eta(x^6 + A)^8 * eta(x^9 + A)), 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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