|
Search: id:A128144
|
|
|
| A128144 |
|
Expansion of chi(-q)* chi(-q^2)* chi(-q^9)/( chi(-q^3)* chi(q^9)) in powers of q where chi() is a Ramanujan theta function. |
|
+0
3
|
|
| 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, 0, -122, -14, 133, 0, -148, 0, 163, 14, -182, 0, 217, 0, -216
(list; graph; listen)
|
|
|
OFFSET
|
0,10
|
|
|
FORMULA
|
Expansion of (eta(q)* eta(q^6)* eta(q^36)* eta(q^9)^2)/(eta(q^3)* eta(q^4)* eta(q^18)^3) in powers of q.
Euler transform of period 36 sequence [ -1, -1, 0, 0, -1, -1, -1, 0, -2, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, -1, -1, -2, 0, -1, -1, -1, 0, 0, -1, -1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= (1-v)*(1-v+v^2)*(2*u-u^2)^2 -(u+v-u*v)^2*(u-v)^2.
a(6n+4)=0. a(6n)=0 if n>0.
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)*eta(x^36+A)*eta(x^9+A)^2/ (eta(x^3+A)*eta(x^4+A)*eta(x^18+A)^3), n))}
|
|
CROSSREFS
|
A092848(n)=-a(6n+2). A128143(n)=-a(n) if n>0. A128145(n)=-a(n) if n>0.
Sequence in context: A095704 A163496 A092241 this_sequence A128145 A128143 A027640
Adjacent sequences: A128141 A128142 A128143 this_sequence A128145 A128146 A128147
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Feb 16 2007
|
|
|
Search completed in 0.011 seconds
|
