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!)
 A255318 Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions. 8
 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 2, 1, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 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 f(x^3) * f(-x^6) / chi(-x^2) in powers of x where chi(), f() are Ramanujan theta functions. Expansion of q^(-11/24) * eta(q^4) * eta(q^6)^4 / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q. Euler transform of period 12 sequence [ 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, -2, ...]. EXAMPLE G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10 + x^11 + 2*x^13 + ... G.f. = q^11 + q^59 + q^83 + q^107 + q^131 + q^179 + q^227 + q^251 + q^275 + ... MATHEMATICA a[ n_] := SeriesCoefficient[QPochhammer[-x^3]*QPochhammer[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^4 + A) * eta(x^6 + A)^4 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))}; CROSSREFS Sequence in context: A060953 A339367 A082858 * A249223 A115953 A225245 Adjacent sequences:  A255315 A255316 A255317 * A255319 A255320 A255321 KEYWORD nonn AUTHOR Michael Somos, Feb 21 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 June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)