|
Search: id:A143062
|
|
|
| A143062 |
|
Expansion of false theta series variation of Euler's pentagonal number series in powers of x. |
|
+0
4
|
|
| 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 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, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
REFERENCES
|
G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See Section 9.4, pp. 232-236
S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41
|
|
FORMULA
|
a(n) = b(24n + 1) where b(n) is multiplicative and b(p^(2e)) = (-1)^e if p = 5 (mod 6), b(p^(2e)) = +1 if p = 1 (mod 6) and b(p^(2e-1)) = b(2^e) = b(3^e) = 0 if e>0.
G.f.: Sum_{k>=0} x^((3*k^2 + k) / 2) * (1 - x^(2*k + 1)) = 1 - Sum_{k>0} x^((3*k^2 - k) / 2) * (1 - x^k).
G.f.: 1 - x / (1 + x) + x^3 / ((1 + x) * (1 + x^2)) - x^6 / ((1 + x) * (1 + x^2) * (1 + x^3)) + ...
|
|
EXAMPLE
|
q - q^25 + q^49 - q^121 + q^169 - q^289 + q^361 - q^529 + q^625 - q^841 + ...
|
|
PROGRAM
|
(PARI) {a(n) = if( issquare( 24*n + 1, &n), (-1)^(n \ 3) )}
|
|
CROSSREFS
|
Cf. A010815.
Sequence in context: A080995 A121373 A133985 this_sequence A074910 A115356 A115359
Adjacent sequences: A143059 A143060 A143061 this_sequence A143063 A143064 A143065
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Jul 21 2008
|
|
|
Search completed in 0.002 seconds
|
