|
|
A208605
|
|
Expansion of q * psi(q^8) / phi(q) in powers of q where phi(), psi() are Ramanujan theta functions.
|
|
3
|
|
|
1, -2, 4, -8, 14, -24, 40, -64, 101, -156, 236, -352, 518, -752, 1080, -1536, 2162, -3018, 4180, -5744, 7840, -10632, 14328, -19200, 25591, -33932, 44776, -58816, 76918, -100176, 129952, -167936, 216240, -277476, 354864, -452392, 574958, -728568, 920600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Expansion of eta(q)^2 * eta(q^4)^2 * eta(q^16)^2 / (eta(q^2)^5 * eta(q^8)) in powers of q.
Euler transform of period 16 sequence [ -2, 3, -2, 1, -2, 3, -2, 2, -2, 3, -2, 1, -2, 3, -2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (16 t)) = 1/4 * g(t) where q = exp(2 Pi i t) and g() is g.f. for A208603.
|
|
EXAMPLE
|
q - 2*q^2 + 4*q^3 - 8*q^4 + 14*q^5 - 24*q^6 + 40*q^7 - 64*q^8 + 101*q^9 + ...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[eta[q]^2* eta[q^4]^2*eta[q^16]^2/(eta[q^2]^5*eta[q^8]), {q, 0, n}]; Table[a[n], {n, 1, 50}] (* G. C. Greubel, Jan 23 2018 *)
|
|
PROG
|
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^16 + A)^2 / (eta(x^2 + A)^5 * eta(x^8 + A)), n))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|