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!)
 A121361 Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions. 19
 1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 1, 3, 0, 0, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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^(-7/12) * eta(q^2) * eta(q^3) * eta(q^4) * eta(q^12) / (eta(q) * eta(q^6)) in powers of q. Euler transform of period 12 sequence [ 1, 0, 0, -1, 1, 0, 1, -1, 0, 0, 1, -2, ...]. 2*a(n) = A093829(12*n + 7). EXAMPLE G.f. = 1 + x + x^2 + x^3 + x^5 + x^6 + 2*x^7 + x^8 + x^10 + x^11 + ... G.f. = q^7 + q^19 + q^31 + q^43 + q^67 + q^79 + 2*q^91 + q^103 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x^1, x^6] QPochhammer[ -x^5, x^6] QPochhammer[ x^6] EllipticTheta[ 2, 0, x] / (2 x^(1/4)), {x, 0, n}]; (* Michael Somos, Sep 02 2014 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^6 + A)), n))}; CROSSREFS Cf. A093829. Sequence in context: A212210 A127499 A198068 * A191907 A052343 A073484 Adjacent sequences:  A121358 A121359 A121360 * A121362 A121363 A121364 KEYWORD nonn AUTHOR Michael Somos, Jul 16 2006 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 1 13:51 EDT 2021. Contains 346391 sequences. (Running on oeis4.)