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 A227175 Expansion of (phi(x) / f(-x^4))^4 in powers of x where phi(), f() are Ramanujan theta functions. 1
 1, 8, 24, 32, 28, 80, 192, 192, 134, 408, 864, 800, 568, 1520, 3072, 2752, 1809, 4808, 9456, 8192, 5316, 13616, 26112, 22144, 13990, 35376, 66624, 55584, 34696, 86016, 159744, 131392, 80724, 198256, 363720, 295776, 180068, 436816, 793344, 638976, 384940 (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 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(2/3) * (eta(q^2)^5 / (eta(q)^2 * eta(q^4)^3))^4 in powers of q. Euler transform of period 4 sequence [ 8, -12, 8, 0, ...]. a(2*n + 1) = 8 * A022569(n). Convolution square of A227033. EXAMPLE 1 + 8*x + 24*x^2 + 32*x^3 + 28*x^4 + 80*x^5 + 192*x^6 + 192*x^7 + 134*x^8 + ... q^-2 + 8*q + 24*q^4 + 32*q^7 + 28*q^10 + 80*q^13 + 192*q^16 + 192*q^19 + ... MATHEMATICA a[ n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q]/QPochhammer[q^4])^4, {q, 0, n}]; PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 / (eta(x + A)^2 * eta(x^4 + A)^3))^4, n))} CROSSREFS Cf. A022569, A227033. Sequence in context: A096727 A028660 A028644 * A340930 A269420 A056196 Adjacent sequences:  A227172 A227173 A227174 * A227176 A227177 A227178 KEYWORD nonn AUTHOR Michael Somos, Jul 03 2013 STATUS approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)