|
Search: id:A134132
|
|
|
| A134132 |
|
Expansion of q^(-1/6) * eta(q^2) * eta(q^3)^2 * eta(q^18) / ( eta(q) * eta(q^6)^2 * eta(q^9) ) in powers of q. |
|
+0
2
|
|
| 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 2, 3, 3, 3, 2, 2, 3, 5, 6, 5, 4, 4, 6, 9, 10, 9, 8, 8, 11, 14, 16, 15, 13, 14, 18, 24, 26, 25, 22, 23, 29, 36, 40, 38, 36, 38, 46, 56, 61, 60, 56, 59, 70, 84, 92, 90, 86, 90, 106, 125, 135, 134, 130, 136, 157, 181, 196, 195, 191, 201, 228, 263, 282
(list; graph; listen)
|
|
|
OFFSET
|
0,8
|
|
|
FORMULA
|
Expansion of (chi(-q) * chi(-q^9) / chi(-q^3)^2)^(-1) in power of q where chi() is a Ramanujan theta function.
Euler transform of period 18 sequence [ 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, ...].
Given g.f. A(x) then B(x) = A(x^6) * x satisfies 0 = f(B(x), B(x^2), B(x^4) ) where f(u, v, w) = (u^2 + v) * w^2 - (u^2 - v) * v.
Given g.f. A(x) then B(x) = A(x^3)^2 * x satisfies 0 = f(B(x), B(x^2)) where f(u, v) = (u - v^2) * (u^2 - v) * (1 + u * v) - (2 * u * v)^2.
G.f. is a period 1 Fourier series which satisfies f(-1 / (648 t)) = 1 / f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 + x^k) * (1 + x^(9*k)) / (1 + x^(3*k))^2.
|
|
EXAMPLE
|
q + q^7 + q^13 + q^31 + q^37 + 2*q^43 + q^49 + q^55 + q^61 + 2*q^67 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^18 + A) / ( eta(x + A) * eta(x^6 + A)^2 * eta(x^9 + A) ), n))}
|
|
CROSSREFS
|
A112178(3*n+1) = -a(n). Convolution inverse of A134131.
Sequence in context: A114731 A035389 A129176 this_sequence A030424 A145515 A026519
Adjacent sequences: A134129 A134130 A134131 this_sequence A134133 A134134 A134135
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Oct 10 2007, Oct 21 2007
|
|
|
Search completed in 0.002 seconds
|
