login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298931 Expansion of psi(x^4) * c(x^3) / (3*x) where phi() is a Ramanujan theta function and c() is a cubic AGM theta function. 3
1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 2, 0, 3, 0, 0, 2, 2, 0, 4, 1, 0, 0, 2, 0, 4, 0, 0, 4, 1, 0, 6, 2, 0, 0, 2, 0, 5, 0, 0, 3, 3, 0, 6, 1, 0, 0, 4, 0, 6, 0, 0, 4, 5, 0, 4, 3, 0, 0, 2, 0, 8, 0, 0, 4, 3, 0, 6, 3, 0, 0, 4, 0, 9, 0, 0, 6, 4, 0, 6, 2, 0, 0, 4, 0, 6, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-3/2) * eta(q^8)^2 * eta(q^9)^3 / (eta(q^3) * eta(q^4)) in powers of q.

Euler transform of a period 72 sequence.

A005872(2*n + 3) = 6*a(n). a(3*n) = A298932(n). a(3*n + 1) = A263452(n-1). a(3*n + 2) = a(4*n + 1) = 0.

EXAMPLE

G.f. = q^3 + q^9 + q^11 + 2*q^15 + q^17 + 2*q^23 + 3*q^27 + 2*q^33 + ...

G.f. = 1 + x^3 + x^4 + 2*x^6 + x^7 + 2*x^10 + 3*x^12 + 2*x^15 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^8]^2 QPochhammer[ x^9]^3 / (QPochhammer[ x^3] QPochhammer[ x^4]), {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^8 + A)^2 * eta(x^9 + A)^3 / (eta(x^3 + A) * eta(x^4 + A)), n))};

CROSSREFS

Cf. A005872, A263452, A298932.

Sequence in context: A113063 A123477 A035225 * A035219 A245716 A241425

Adjacent sequences:  A298928 A298929 A298930 * A298932 A298933 A298934

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 29 2018

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 31 18:30 EDT 2020. Contains 333151 sequences. (Running on oeis4.)