|
|
A258771
|
|
Expansion of psi(-x) * phi(x)^4 in powers of x where phi(), psi() are Ramanujan theta functions.
|
|
3
|
|
|
1, 7, 16, 7, -16, 0, 17, -48, -64, 16, 1, -16, 16, -32, 32, 55, -48, 64, 64, 16, 128, -9, -80, -32, 16, 48, -80, 96, 49, -144, -16, -144, -64, -64, -96, 144, 33, -64, -160, 0, 112, 32, 32, -96, 128, -25, 0, 32, -160, 304, 144, 96, 144, -48, 48, 119, 16, -256
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Expansion of q^(-1/8) * eta(q^2)^19 / (eta(q) * eta(q^4))^7 in powers of q.
Euler transform of period 4 sequence [ 7, -12, 7, -5, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (256 t)) = 1024 (t/i)^(5/2) f(t) where q = exp(2 Pi i t).
|
|
EXAMPLE
|
G.f. = 1 + 7*x + 16*x^2 + 7*x^3 - 16*x^4 + 17*x^6 - 48*x^7 - 64*x^8 + ...
G.f. = q + 7*q^9 + 16*q^17 + 7*q^25 - 16*q^33 + 17*q^49 - 48*q^57 + ...
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[EllipticTheta[ 3, 0, x]^4 QPochhammer[ x] / QPochhammer[ x^2, x^4], {x, 0, n}];
|
|
PROG
|
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^19 / (eta(x + A) * eta(x^4 + A) )^7, n))};
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|