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!)
 A208457 Expansion of x * f(-x) * f(-x^12)^3 * psi(-x^3) / psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions. 2
 0, 1, -1, -2, 0, 3, 2, -4, 0, 5, -1, -8, 0, 7, 4, -8, 0, 9, -8, -10, 0, 14, 6, -12, 0, 16, -6, -14, 0, 15, 8, -20, 0, 17, -14, -18, 0, 19, 10, -24, 0, 26, -1, -22, 0, 23, 16, -28, 0, 25, -20, -32, 0, 32, 14, -28, 0, 29, -12, -30, 0, 38, 16, -32, 0, 33, -31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-2/3) * eta(q) * eta(q^2) * eta(q^3) * eta(q^12)^4 / (eta(q^4)^2 * eta(q^6)) in powers of q. Euler transform of period 12 sequence [-1, -2, -2, 0, -1, -2, -1, 0, -2, -2, -1, -4, ...]. a(4*n) = 0. a(n) = -(-1)^n * A208435(n). EXAMPLE G.f. = x - x^2 - 2*x^3 + 3*x^5 + 2*x^6 - 4*x^7 + 5*x^9 - x^10 - 8*x^11 + ... G.f. = q^5 - q^8 - 2*q^11 + 3*q^17 + 2*q^20 - 4*q^23 + 5*q^29 - q^32 - 8*q^35 + ... MATHEMATICA QP:= QPochhammer; Join[{0}, CoefficientList[Series[Simplify[QP[q]* QP[q^2]*QP[q^3]*QP[q^12]^4/(QP[q^4]^2*QP[q^6]), q > 0], {q, 0, 50}], q]] (* G. C. Greubel, Aug 12 2018 *) PROG (PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)^4 / (eta(x^4 + A)^2 * eta(x^6 + A)), n))}; CROSSREFS Cf. A208435. Sequence in context: A298932 A089196 A208435 * A232343 A140944 A057860 Adjacent sequences:  A208454 A208455 A208456 * A208458 A208459 A208460 KEYWORD sign AUTHOR Michael Somos, Feb 26 2012 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 23 13:59 EDT 2021. Contains 345402 sequences. (Running on oeis4.)