|
Search: id:A116915
|
|
|
| A116915 |
|
Expansion of f(-x,-x^4)^2/f(-x,-x^2) in powers of x. |
|
+0
2
|
|
| 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
|
|
FORMULA
|
Euler transform of period 5 sequence [ -1, 1, 1, -1, -1,...].
G.f.: Sum_{k} (-1)^k(x^((15k^2-7k)/2) -x^((15k^2+13k)/2+1)).
G.f.: Product_{k>0} (1-x^(5k))(1-x^(5k-1))(1-x^(5k-4))/((1-x^(5k-2))(1-x^(5k-3))).
|
|
PROGRAM
|
(PARI) {a(n)=n=5*n+2; if(issquare(24*n+1, &n), -kronecker(12, n))}
(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, (1-x^k)^((k%5==0)+ kronecker(5, k)), 1+x*O(x^n)), n))}
|
|
CROSSREFS
|
Cf. A010815(5n+2)=-a(n).
Sequence in context: A115944 A071003 A113431 this_sequence A076141 A011751 A093709
Adjacent sequences: A116912 A116913 A116914 this_sequence A116916 A116917 A116918
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Feb 26 2006
|
|
|
Search completed in 0.002 seconds
|
