|
Search: id:A113431
|
|
|
| A113431 |
|
Expansion of f(-x)f(-x^10)/f(-x^4,-x^6) in powers of x. |
|
+0
1
|
|
| 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
|
|
|
FORMULA
|
Euler transform of period 10 sequence [ -1, -1, -1, 0, -1, 0, -1, -1, -1, -1, ...].
G.f.: Prod_{k>0} (1-x^k)/((1-x^(10k-4))(1-x^(10k-6))) = Sum_{k} x^((15k^2+7k)/2) -x^((15k^2+13k+2)/2).
f(a,b)=Sum_{k} a^((k^2+k)/2)*b^((k^2-k)/2) is Ramanujan's two-variable theta function.
|
|
PROGRAM
|
(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, n, 1-x^k*[1, 1, 1, 1, 0, 1, 0, 1, 1, 1][k%10+1], 1+x*O(x^n)), n))}
|
|
CROSSREFS
|
Sequence in context: A115944 A071003 A071002 this_sequence A116915 A076141 A011751
Adjacent sequences: A113428 A113429 A113430 this_sequence A113432 A113433 A113434
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Oct 31 2005
|
|
|
Search completed in 0.002 seconds
|
