|
Search: id:A132967
|
|
|
| A132967 |
|
Expansion of q * chi(-q^3) * chi(-q^5) / ( chi(-q^2) * chi(-q^30) ) in powers of q where chi() is a Ramanaujan theta function. |
|
+0
2
|
|
| 1, 0, 1, -1, 1, -2, 2, -2, 3, -4, 4, -5, 6, -6, 9, -11, 10, -14, 16, -17, 22, -24, 26, -32, 37, -40, 47, -54, 58, -70, 80, -84, 100, -112, 122, -143, 158, -172, 198, -222, 242, -274, 306, -332, 379, -422, 454, -515, 569, -620, 698, -766, 834, -932, 1028, -1118, 1240, -1364, 1480, -1645, 1806, -1952
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
FORMULA
|
Expansion of eta(q^3) * eta(q^4) * eta(q^5) * eta(q^60) / ( eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30) ) in powers of q.
Euler transform of period 60 sequence [ 0, 1, -1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 1, -1, 0, 0, 2, 0, 0, -1, 1, -1, 0, 0, 1, -1, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 1, 0, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = 1 - f(t) where q = exp(2 pi i t).
G.f.: x * Product_{k>0} (1 + x^(2*k)) * (1 + x^(30*k)) / ( (1 + x^(3*k)) * (1 + x^(5*k)) ).
|
|
EXAMPLE
|
q + q^3 - q^4 + q^5 - 2*q^6 + 2*q^7 - 2*q^8 + 3*q^9 - 4*q^10 + 4*q^11 - ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x*O(x^n); polcoeff( eta(x^3 + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^60 + A) / eta(x^2 + A) / eta(x^6 + A) / eta(x^10 + A) / eta(x^30 + A), n))}
|
|
CROSSREFS
|
A132968(n) = -a(n) unless n=0.
Sequence in context: A053254 A067357 A051059 this_sequence A132968 A029075 A029052
Adjacent sequences: A132964 A132965 A132966 this_sequence A132968 A132969 A132970
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Sep 02 2007
|
|
|
Search completed in 0.002 seconds
|
