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 A146164 Expansion of f(-x^4) * chi(x^5) / f(-x^5) in powers of x where f(), chi() are Ramanujan theta functions. 4
 1, 0, 0, 0, -1, 2, 0, 0, -1, -2, 3, 0, 0, -2, -3, 6, 0, 0, -3, -6, 11, 0, 0, -6, -10, 18, 0, 0, -9, -16, 28, 0, 0, -14, -25, 44, 0, 0, -22, -38, 67, 0, 0, -32, -57, 100, 0, 0, -48, -84, 146, 0, 0, -70, -121, 210, 0, 0, -99, -172, 299, 0, 0, -140, -243, 420, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 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^(1/4) * eta(q^4) * eta(q^10)^2 / (eta(q^5)^2 * eta(q^20)) in powers of q. Euler transform of period 20 sequence [ 0, 0, 0, -1, 2, 0, 0, -1, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = (5/4)^(1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A146162. a(5*n + 1) = a(5*n + 2) = 0. a(n) = A138532(2*n + 1). a(5*n + 4) = - A146163(n). Convolution inverse of A146165. EXAMPLE G.f. = 1 - x^4 + 2*x^5 - x^8 - 2*x^9 + 3*x^10 - 2*x^13 - 3*x^14 + 6*x^15 + ... G.f. = 1/q - q^15 + 2*q^19 - q^31 - 2*q^35 + 3*q^39 - 2*q^51 - 3*q^55 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ x^4] QPochhammer[ -x^5, x^10] / QPochhammer[ x^5], {x, 0, n}]; (* Michael Somos, Sep 03 2015 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^10 + A)^2 / (eta(x^5 + A)^2 * eta(x^20 + A)), n))}; CROSSREFS Cf. A138532, A146162, A146163, A146165. Sequence in context: A111755 A144528 A290694 * A263141 A051510 A340958 Adjacent sequences:  A146161 A146162 A146163 * A146165 A146166 A146167 KEYWORD sign AUTHOR Michael Somos, Oct 27 2008, Nov 10 2008 EXTENSIONS Edited by N. J. A. Sloane, Nov 21 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified July 30 09:18 EDT 2021. Contains 346359 sequences. (Running on oeis4.)