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 A259358 Expansion of f(-x^5)^2 / f(-x^2, -x^3) in powers of x where f(,) is the Ramanujan general theta function. 2
 1, 0, 1, 1, 1, 0, 2, 1, 2, 2, 2, 2, 3, 2, 4, 4, 5, 4, 6, 5, 7, 7, 8, 8, 11, 10, 12, 13, 15, 14, 18, 17, 21, 21, 24, 25, 29, 29, 34, 35, 39, 40, 47, 47, 53, 55, 61, 63, 72, 73, 82, 86, 94, 97, 109, 112, 124, 129, 141, 147, 162, 167, 183, 192, 208, 217, 237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). Rogers-Ramanujan functions: G(q) (see A003114), H(q) (A003106). REFERENCES G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook, Part III, Springer, 2012, see p. 12, Entry 2.1.3, Equation (2.1.22). Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 23, equation 4. LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of f(-x^5) * f(-x, -x^4) / f(-x) in powers of x where f(,) is the Ramanujan general theta function. Expansion of f(-x^5) * H(x) in powers of x where f() is a Ramanujan theta funcation and H() is a Rogers-Ramanujan function. - Michael Somos, Jul 09 2015 Euler transform of period 5 sequence [ 0, 1, 1, 0, -1, ...]. G.f.: Product_{k>0} (1 - x^(5*k)) / ((1 - x^(5*k-3)) * (1 - x^(5*k-2))). Convolution of A035959 and A113429. EXAMPLE G.f. = 1 + x^2 + x^3 + x^4 + 2*x^6 + x^7 + 2*x^8 + 2*x^9 + 2*x^10 + ... G.f. = q^47 + q^287 + q^407 + q^527 + 2*q^767 + q^887 + 2*q^1007 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ x^5] / (QPochhammer[ x^2, x^5] QPochhammer[ x^3, x^5]), {x, 0, n}]; PROG (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[ 1, 0, -1, -1, 0][k%5+1]), n))}; CROSSREFS Cf. A035959, A113429, A259357. Sequence in context: A241065 A086376 A160089 * A290086 A129363 A303399 Adjacent sequences:  A259355 A259356 A259357 * A259359 A259360 A259361 KEYWORD nonn AUTHOR Michael Somos, Jun 24 2015 STATUS approved

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Last modified January 22 08:24 EST 2019. Contains 319357 sequences. (Running on oeis4.)