|
Search: id:A121362
|
|
|
| A121362 |
|
Expansion of eta(q)*eta(q^6)*eta(q^10)*eta(q^15)/(eta(q^3)*eta(q^5)) in powers of q. |
|
+0
4
|
|
| 1, -1, -1, 1, -1, 1, 0, -1, 1, 1, 0, -1, 0, 0, 1, 1, -2, -1, 2, -1, 0, 0, -2, 1, 1, 0, -1, 0, 0, -1, 2, -1, 0, 2, 0, 1, 0, -2, 0, 1, 0, 0, 0, 0, -1, 2, -2, -1, 1, -1, 2, 0, -2, 1, 0, 0, -2, 0, 0, 1, 2, -2, 0, 1, 0, 0, 0, -2, 2, 0, 0, -1, 0, 0, -1, 2, 0, 0, 2, -1, 1, 0, -2, 0, 2, 0, 0, 0, 0, 1, 0, -2, -2, 2, -2, 1, 0, -1, 0, 1, 0, -2, 0, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
1,17
|
|
|
FORMULA
|
Euler transform of period 30 sequence [ -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -2, ...].
Expansion of q*f(-q)f(-q^15)/(chi(-q^3)chi(-q^5)) in powers of q where f(),chi() are Ramanujan theta functions.
G.f.: x Product_{n>0} (1-x^n)(1+x^(3n))(1+x^(5n))(1-x^(15n)).
a(n) is multiplicative with a(2^e)=a(3^e)=a(5^e)=(-1)^e, a(p^e) = e+1 if p == 1,4 (mod 15), a(p^e) = (-1)^e*(e+1) if p == 2,8 (mod 15), a(p^e) = (1+( -1)^e)/2 if p == 7,11,13,14 (mod 15).
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)*eta(x^10+A)*eta(x^15+A)/(eta(x^3+A)*eta(x^5+A)), n))}
|
|
CROSSREFS
|
Cf. A082451(n)=|a(n)|.
Sequence in context: A048622 A105661 A082451 this_sequence A091704 A123739 A165575
Adjacent sequences: A121359 A121360 A121361 this_sequence A121363 A121364 A121365
|
|
KEYWORD
|
sign,mult
|
|
AUTHOR
|
Michael Somos, Jul 22 2006
|
|
|
Search completed in 0.002 seconds
|
