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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279955 Expansion of chi(-x^4)^4 * f(-x^4)^2 * f(-x)^2 in powers of x where chi(), f() are Ramanujan theta functions. 5
1, -2, -1, 2, -5, 14, 4, -12, 5, -40, 0, 26, 11, 68, -15, -30, -18, -106, 3, 50, -10, 182, 29, -104, 10, -270, 11, 130, 37, 360, -51, -164, -16, -506, -30, 266, -65, 686, 62, -320, 53, -898, 22, 414, 50, 1206, -61, -612, -52, -1560, -4, 696, -81, 1958, 120 (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
Amanda Clemm, Modular Forms and Weierstrass Mock Modular Forms, Mathematics, volume 4, issue 1, (2016)
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q * eta(q^4)^2 * eta(q^16)^6 / eta(q^32)^4 in powers of q^4.
Euler transform of period 8 sequence [ -2, -2, -2, -8, -2, -2, -2, -4, ...].
a(n) = (-1)^n * A280339(n).
a(3*n + 1) / a(1) == A002171(n) (mod 3). a(3^3*n + 7) / a(7) == A002171(n) (mod 3^2).
EXAMPLE
G.f. = 1 - 2*x - x^2 + 2*x^3 - 5*x^4 + 14*x^5 + 4*x^6 - 12*x^7 + 5*x^8 + ...
G.f. = q^-1 - 2*q^3 - q^7 + 2*q^11 - 5*q^15 + 14*q^19 + 4*q^23 - 12*q^27 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^4]^2 QPochhammer[ x^4, x^8]^4, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^6 / eta(x^8 + A)^4, n))};
CROSSREFS
Sequence in context: A327194 A160457 A107087 * A280339 A115141 A031148
KEYWORD
sign
AUTHOR
Michael Somos, Dec 23 2016
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)