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 A279955 Expansion of chi(-x^4)^4 * f(-x^4)^2 * f(-x)^2 in powers of x where chi(), f() are Ramanujan theta functions. 5
 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..1000 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 q * eta(q^4)^2 * eta(q^16)^6 / eta(q^32)^4 in powers of q^4. Euler transform of period 8 sequence [ -2, -2, -2, -8, -2, -2, -2, -4, ...]. a(n) = (-1)^n * A280339(n). a(3*n + 1) / a(1) == A002171(n) (mod 3). a(3^3*n + 7) / a(7) == A002171(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[ QPochhammer[ x]^2 QPochhammer[ x^4]^2 QPochhammer[ x^4, x^8]^4, {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^6 / eta(x^8 + A)^4, n))}; CROSSREFS Cf. A002171, A280339. Sequence in context: A327194 A160457 A107087 * A280339 A115141 A031148 Adjacent sequences: A279952 A279953 A279954 * A279956 A279957 A279958 KEYWORD sign AUTHOR Michael Somos, Dec 23 2016 STATUS approved

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Last modified June 8 02:04 EDT 2023. Contains 363157 sequences. (Running on oeis4.)