This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224822 Expansion of phi(-q) * phi(-q^3)^2 in powers of q where phi() is a Ramanujan theta function. 2
 1, -2, 0, -4, 10, 0, 4, -16, 0, -2, 8, 0, 12, -8, 0, -16, 26, 0, 0, -24, 0, -8, 8, 0, 20, -10, 0, -4, 32, 0, 8, -48, 0, -8, 16, 0, 10, -8, 0, -32, 40, 0, 8, -24, 0, 0, 16, 0, 28, -18, 0, -24, 40, 0, 4, -64, 0, -8, 8, 0, 32, -24, 0, -16, 58, 0, 16, -24, 0, -16 (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 eta(q)^2 * eta(q^3)^4 / (eta(q^2) * eta(q^6)^2) in powers of q. Euler transform of period 6 sequence [-2, -1, -6, -1, -2, -3, ...]. G.f.: (Sum_{k in Z} (-1)^k * x^k^2) * (Sum_{k in Z} (-1)^k * x^(3*k^2))^2. a(3*n + 2) = 0. a(2*n) = A028967(n). a(3*n) = A224821(n). EXAMPLE G.f. = 1 - 2*q - 4*q^3 + 10*q^4 + 4*q^6 - 16*q^7 - 2*q^9 + 8*q^10 + 12*q^12 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] EllipticTheta[ 4, 0, q^3]^2, {q, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^3 + A)^4 / (eta(x^2 + A) * eta(x^6 + A)^2), n))}; CROSSREFS Cf. A028967, A224821. Sequence in context: A077119 A002938 A111938 * A246928 A167341 A214199 Adjacent sequences:  A224819 A224820 A224821 * A224823 A224824 A224825 KEYWORD sign AUTHOR Michael Somos, Jul 20 2013 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 18:34 EDT 2019. Contains 323534 sequences. (Running on oeis4.)