|
|
A260163
|
|
Expansion of f(x^2)^2 / f(-x) in powers of x where f() is a Ramanujan theta function.
|
|
1
|
|
|
1, 1, 4, 5, 8, 12, 17, 24, 36, 48, 65, 88, 116, 152, 200, 257, 328, 420, 532, 668, 840, 1045, 1296, 1604, 1972, 2416, 2952, 3592, 4357, 5272, 6356, 7640, 9168, 10964, 13080, 15576, 18497, 21920, 25932, 30604, 36048, 42392, 49752, 58288, 68184, 79617, 92820
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Expansion of q^(-1/8) * eta(q^4)^6 / (eta(q) * eta(q^2)^2 * eta(q^8)^2) in powers of q.
Euler transform of period 8 sequence [ 1, 3, 1, -3, 1, 3, 1, -1, ...].
|
|
EXAMPLE
|
G.f. = 1 + x + 4*x^2 + 5*x^3 + 8*x^4 + 12*x^5 + 17*x^6 + 24*x^7 + 36*x^8 + ...
G.f. = q + q^9 + 4*q^17 + 5*q^25 + 8*q^33 + 12*q^41 + 17*q^49 + 24*q^57 + ...
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2]^2 / QPochhammer[ x], {x, 0, n}];
|
|
PROG
|
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^6 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^2), n))};
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|