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 A261576 Expansion of 3 * b(q^2) * c(q^2) / c(q)^2 in powers of q where b(), c() are cubic AGM theta functions. 2
 1, -2, -3, 12, -10, -18, 60, -48, -75, 228, -172, -252, 732, -524, -744, 2088, -1450, -1998, 5460, -3704, -4986, 13344, -8872, -11736, 30876, -20206, -26322, 68268, -44080, -56682, 145224, -92672, -117867, 298800, -188756, -237744, 597108, -373852, -466836 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882). Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS 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 FORMULA Expansion of f(-q^2)^4 / (f(-q^3)^2 * f(q, q^2)^2) in powers of q where f(,) is Ramanujan's general theta function. Expansion of (eta(q) * eta(q^2) * eta(q^6) / eta(q^3)^3)^2 in powers of q. Euler transform of period 6 sequence [ -2, -4, 4, -4, -2, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (18 t)) = 9/4 g(t) where q = exp(2 Pi i t) and g() is the g.f. of A258099. a(n) = A261326(2*n).  a(3*n + 2) = -3 * A233698(n). EXAMPLE G.f. = 1 - 2*x - 3*x^2 + 12*x^3 - 10*x^4 - 18*x^5 + 60*x^6 - 48*x^7 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (QPochhammer[ q] QPochhammer[ q^2] QPochhammer[ q^6] / QPochhammer[ q^3]^3)^2, {q, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^2 + A) * eta(x^6 + A) / eta(x^3 + A)^3)^2, n))}; CROSSREFS Cf. A233698, A258099, A261326. Sequence in context: A225723 A092972 A334914 * A081526 A075711 A079077 Adjacent sequences:  A261573 A261574 A261575 * A261577 A261578 A261579 KEYWORD sign AUTHOR Michael Somos, Aug 25 2015 STATUS approved

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Last modified June 16 21:43 EDT 2021. Contains 345080 sequences. (Running on oeis4.)