|
| |
|
|
A213266
|
|
Expansion of psi(q) * psi(q^9) / (psi(q^2) * chi(q^3) * psi(-q^9)) in powers of q where psi(), chi() are Ramanujan theta functions.
|
|
2
|
|
|
|
1, 1, -1, -1, 0, 1, 0, -1, 1, 2, 0, -3, 0, 2, 0, -3, 0, 5, 0, -4, -2, 4, 0, -5, 0, 7, 2, -7, 0, 5, 0, -10, 1, 12, 0, -10, 0, 14, -4, -17, 0, 21, 0, -22, 4, 24, 0, -34, 0, 33, 1, -36, 0, 45, 0, -45, -8, 52, 0, -55, 0, 62, 8, -71, 0, 70, 0, -88, 2, 96, 0, -98
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,10
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Expansion of eta(q^2)^3 * eta(q^3) * eta(q^12) * eta(q^18)^3 / (eta(q) * eta(q^4)^2 * eta(q^6)^2 * eta(q^9)^2 * eta(q^36)) in powers of q.
Euler transform of period 36 sequence [ 1, -2, 0, 0, 1, -1, 1, 0, 2, -2, 1, 0, 1, -2, 0, 0, 1, -2, 1, 0, 0, -2, 1, 0, 1, -2, 2, 0, 1, -1, 1, 0, 0, -2, 1, 0, ...].
a(n) = A182038(n) unless n=0. a(6*n) = 0 unless n=0. a(6*n + 4) = 0. a(6*n + 2) = -A092848(n).
|
|
|
EXAMPLE
|
1 + q - q^2 - q^3 + q^5 - q^7 + q^8 + 2*q^9 - 3*q^11 + 2*q^13 - 3*q^15 + ...
|
|
|
MATHEMATICA
|
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[eta[q^2]^3* eta[q^3]*eta[q^12]*eta[q^18]^3/(eta[q]*eta[q^4]^2*eta[q^6]^2*eta[q^9]^2*eta[q^36]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 19 2018 *)
|
|
|
PROG
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^3 + A) * eta(x^12 + A) * eta(x^18 + A)^3 / (eta(x + A) * eta(x^4 + A)^2 * eta(x^6 + A)^2 * eta(x^9 + A)^2 * eta(x^36 + A)), n))}
(PARI) q='q+O('q^99); Vec(eta(q^2)^3*eta(q^3)*eta(q^12)*eta(q^18)^3 /(eta(q)*eta(q^4)^2*eta(q^6)^2*eta(q^9)^2*eta(q^36))) \\ Altug Alkan, Mar 20 2018
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
