The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A255258 Expansion of q^2 * phi(q) * psi(q^16) in powers of q where phi(), psi() are Ramanujan theta functions. 2
 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 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 = 2..2500 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2)^5 * eta(q^32)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^16)) in powers of q. Euler transform of period 32 sequence [ 2, -3, 2, -1, 2, -3, 2, -1, 2, -3, 2, -1, 2, -3, 2, 0, 2, -3, 2, -1, 2, -3, 2, -1, 2, -3, 2, -1, 2, -3, 2, -2, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 8^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A224609. (-1)^n * a(n) = A227395(n). a(4*n) = a(4*n + 1) = a(8*n + 7) = 0. a(4*n + 2) = A113411(n). a(8*n + 3) = 2 * A033761(n). EXAMPLE G.f. = q^2 + 2*q^3 + 2*q^6 + 2*q^11 + 3*q^18 + 2*q^19 + 2*q^22 + 4*q^27 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] EllipticTheta[ 2, 0, q^8] / 2, {q, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<2, 0, n -= 2; A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^32 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^16 + A)), n))}; (Magma) A := Basis( ModularForms( Gamma1(32), 1), 89); A[3] + 2*A[4] + 2*A[7] + 2*A[12]; CROSSREFS Cf. A033761, A113411, A224609, A227395. Sequence in context: A033729 A318984 A227395 * A329266 A260671 A033725 Adjacent sequences: A255255 A255256 A255257 * A255259 A255260 A255261 KEYWORD nonn AUTHOR Michael Somos, Feb 19 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 6 06:14 EDT 2024. Contains 374960 sequences. (Running on oeis4.)