The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A258741 Expansion of f(x^3, x^5) / f(x, x^3) in powers of x where f(, ) is Ramanujan's general theta function. 2
 1, -1, 1, -1, 2, -2, 2, -3, 4, -5, 5, -6, 8, -9, 10, -12, 15, -17, 19, -22, 26, -30, 33, -38, 45, -51, 56, -64, 74, -83, 92, -104, 119, -133, 147, -165, 187, -208, 229, -256, 288, -319, 351, -390, 435, -481, 528, -584, 649, -715, 783, -863, 954, -1047, 1145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41, 16th equation. 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 f(x^4, x^12) / f(x, x^7) where f(, ) is Ramanujan's general theta function. Euler transform of period 16 sequence [ -1, 1, 0, 1, 0, 0, -1, 0, -1, 0, 0, 1, 0, 1, -1, 0, ...]. G.f.: 1 / (Product_{k>=0} (1 + x^(8*k + 1)) * (1 - x^(8*k + 4)) * (1 + x^(8*k + 7))). G.f.: (1 + x^4 + x^12 + x^24 + x^40 + ...) / (1 + x + x^7 + x^10 + x^22 + ...). [Ramanujan] G.f.: 1 - x * (1 - x) / (1 - x^2) + x^4 * (1 - x) * (1 - x^3) / ((1 - x^2) * (1 - x^4)) - ... [Ramanujan] a(n) = (-1)^n * A036016(n) = A029838(2*n) = A082303(2*n). Convolution product of A106507 and A214264. EXAMPLE G.f. = 1 - x + x^2 - x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 3*x^7 + 4*x^8 - 5*x^9 + ... G.f. = 1/q - q^15 + q^31 - q^47 + 2*q^63 - 2*q^79 + 2*q^95 - 3*q^111 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x^4, x^4] / (QPochhammer[ -x, x^8] QPochhammer[ -x^7, x^8]), {x, 0, n}]; a[ n_] := SeriesCoefficient[ 1 / Product[ (1 + x^(8 k + 1)) (1 - x^(8 k + 4)) (1 + x^(8 k + 7)), {k, 0, Ceiling[ n/8]}], {x, 0, n}]; a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{1, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, -1, 1, 0}[[Mod[k, 16, 1]]], {k, n}], {x, 0, n}]; PROG (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[ 0, 1, -1, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, -1, 1][k%16 + 1]), n))}; CROSSREFS Cf. A029838, A036016, A082303, A106507, A214264. Sequence in context: A076872 A008906 A029074 * A036016 A051918 A174740 Adjacent sequences:  A258738 A258739 A258740 * A258742 A258743 A258744 KEYWORD sign AUTHOR Michael Somos, Nov 06 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 03:52 EDT 2021. Contains 346435 sequences. (Running on oeis4.)