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!)
 A248886 Expansion of f(-x, -x) * f(x^2, x^4) in powers of x where f(, ) is Ramanujan's general theta function. 2
 1, -2, 1, -2, 3, -2, 2, 0, 2, -2, 1, -4, 0, -2, 3, -2, 2, 0, 4, -2, 2, 0, 0, -2, 1, -4, 2, -2, 2, -2, 3, -2, 0, -2, 2, -2, 2, 0, 2, -4, 4, 0, 0, 0, 1, -2, 4, 0, 2, -4, 2, -2, 1, -6, 0, -2, 2, 0, 0, -2, 4, -2, 0, -2, 2, 0, 4, 0, 4, -2, 1, -2, 0, -2, 4, 0, 0, -2 (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..2500 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of f(-x)^2 * phi(-x^6) / phi(-x^2) in powers of x where phi(), f() are Ramanujan theta functions. Expansion of phi(-x) * phi(-x^6) / chi(-x^2) in powers of q where phi(), chi() are Ramanujan theta functions. Expansion of q^(-1/12) * eta(q)^2 * eta(q^4) * eta(q^6)^2 / (eta(q^2)^2 * eta(q^12)) in powers of q. Euler transform of period 12 sequence [-2, 0, -2, -1, -2, -2, -2, -1, -2, 0, -2, -2, ...]. a(n) = (-1)^n * A123884(n). a(2*n) = A131961(n). a(2*n + 1) = -2 * A131963(n). EXAMPLE G.f. = 1 - 2*x + x^2 - 2*x^3 + 3*x^4 - 2*x^5 + 2*x^6 + 2*x^8 - 2*x^9 + ... G.f. = q - 2*q^13 + q^25 - 2*q^37 + 3*q^49 - 2*q^61 + 2*q^73 + 2*q^97 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 EllipticTheta[ 4, 0, x^6] / EllipticTheta[ 4, 0, x^2], {x, 0, n}]; a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] EllipticTheta[ 4, 0, x^6] QPochhammer[ -x^2, x^2], {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) * eta(x^6 + A)^2 / (eta(x^2 + A)^2* eta(x^12 + A)), n))}; (PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^4)*eta(q^6)^2/(eta(q^2)^2*eta(q^12))) \\ Altug Alkan, Jul 31 2018 CROSSREFS Cf. A123884, A131961, A131963. Sequence in context: A141662 A328383 A088062 * A123884 A178412 A182598 Adjacent sequences:  A248883 A248884 A248885 * A248887 A248888 A248889 KEYWORD sign AUTHOR Michael Somos, Oct 01 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 May 24 23:45 EDT 2020. Contains 334581 sequences. (Running on oeis4.)