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 A280339 Expansion of phi(x)^2 * chi(x^2)^4 * f(-x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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..5000 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 FORMULA Expansion of phi(-x^4)^2 * chi(-x^4)^2 * f(x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions. Expansion of q^(1/4) * eta(q^2)^6 * eta(q^4)^4 / (eta(q)^2 * eta(q^8)^4) in powers of q. Euler transform of period 8 sequence [2, -4, 2, -8, 2, -4, 2, -4, ...]. a(n) = (-1)^n * A279955(n). a(3*n + 1) / a(1) == A138515(n) (mod 3). a(3^3*n + 7) / a(7) == A138515(n) (mod 3^2). EXAMPLE 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 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, x]^2 QPochhammer[ x]^2 QPochhammer[ -x^2, x^4]^4, {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^6 * eta(x^4 + A)^4 / (eta(x + A)^2 * eta(x^8 + A)^4), n))}; CROSSREFS Cf. A138515, A279955. Sequence in context: A160457 A107087 A279955 * A115141 A031148 A032238 Adjacent sequences:  A280336 A280337 A280338 * A280340 A280341 A280342 KEYWORD sign AUTHOR Michael Somos, Dec 31 2016 STATUS approved

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Last modified July 31 18:05 EDT 2021. Contains 346376 sequences. (Running on oeis4.)