|
| |
|
|
A279365
|
|
Expansion of phi(-x)^2 / chi(-x^5) in powers of x where psi(), chi() are Ramanujan theta functions.
|
|
1
|
|
|
|
1, -4, 4, 0, 4, -7, -4, 4, 4, 0, 1, -4, 4, -4, 0, 2, -4, 0, 0, 4, 2, -4, 0, 4, 0, -1, 0, 4, -4, -4, -8, 0, 4, 4, 4, 1, 0, 0, 0, 4, -2, 0, -4, 0, -4, 0, -4, 0, 0, 4, 2, 4, 0, -4, -4, 8, 0, 4, 0, -4, -1, 0, -4, 0, 0, 2, 0, -4, 4, 0, -2, 4, -4, 0, 0, -1, 0, 0, -4
(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..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
|
Expansion of q^(-5/24) * eta(q)^4 * eta(q^10) / (eta(q^2)^2 * eta(q^5)) in powers of q.
Euler transform of period 10 sequence [ -4, -2, -4, -2, -3, -2, -4, -2, -4, -2, ...].
|
|
|
EXAMPLE
|
G.f. = 1 - 4*x + 4*x^2 + 4*x^4 - 7*x^5 - 4*x^6 + 4*x^7 + 4*x^8 + ...
G.f. = q^5 - 4*q^29 + 4*q^53 + 4*q^101 - 7*q^125 - 4*q^149 + ...
|
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x]^2 / QPochhammer[ x^5, x^10], {x, 0, n}];
|
|
|
PROG
|
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^10 + A) / (eta(x^2 + A)^2 * eta(x^5 + A)), n))};
(PARI) lista(nn) = {q='q+O('q^nn); Vec(eta(q)^4*eta(q^10)/(eta(q^2)^2*eta(q^5)))} \\ Altug Alkan, Mar 21 2018
|
|
|
CROSSREFS
|
Sequence in context: A155836 A337398 A245971 * A164613 A104794 A004018
Adjacent sequences: A279362 A279363 A279364 * A279366 A279367 A279368
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Michael Somos, Dec 10 2016
|
|
|
STATUS
|
approved
|
| |
|
|
