|
|
A259668
|
|
Expansion of psi(-x)^2 * psi(x^3)^2 / (phi(-x^4) * psi(-x^6)) in power of x where phi(), psi() are Ramanujan theta functions.
|
|
7
|
|
|
1, -2, 1, 0, 0, -2, 3, -2, 2, 0, 0, -2, 3, -2, 0, 0, 0, 0, 2, -4, 1, 0, 0, -2, 2, -2, 4, 0, 0, 0, 3, -4, 0, 0, 0, 0, 4, -2, 0, 0, 0, -4, 1, -2, 2, 0, 0, -2, 2, -2, 0, 0, 0, 0, 4, 0, 3, 0, 0, -2, 2, -6, 2, 0, 0, -2, 4, -2, 0, 0, 0, 0, 1, -2, 2, 0, 0, -2, 2, -2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Expansion of f(-x^8) * f(-x, -x^5)^2 / psi(-x^6) in powers of x where psi(), f() are Ramanujan theta functions.
Euler transform of period 24 sequence [ -2, 0, 0, 0, -2, -1, -2, -1, 0, 0, -2, -2, -2, 0, 0, -1, -2, -1, -2, 0, 0, 0, -2, -2, ...].
|
|
EXAMPLE
|
G.f. = 1 - 2*x + x^2 - 2*x^5 + 3*x^6 - 2*x^7 + 2*x^8 - 2*x^11 + 3*x^12 + ...
G.f. = q - 2*q^5 + q^9 - 2*q^21 + 3*q^25 - 2*q^29 + 2*q^33 - 2*q^45 + ...
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[ QPochhammer[ x^8] QPochhammer[x^12, x^24] QPochhammer[ x^6] (QPochhammer[ x, x^6] QPochhammer[ x^5, x^6])^2, {x, 0, n}];
a[ n_] := SeriesCoefficient[ (EllipticTheta[2, 0, x^(3/2)] EllipticTheta[ 2, Pi/4, x^(1/2)])^2 / (2^(5/2) x^(1/4) EllipticTheta[ 4, 0, x^4] EllipticTheta[ 2, Pi/4, x^3]), {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^6 + A)^3 * eta(x^8 + A) * eta(x^12 + A) / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^24 + A)), n))};
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|