|
Search: id:A111317
|
|
|
| A111317 |
|
Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q^2,q^3)/qf(q,q^3). |
|
+0
3
|
|
| 1, 1, 0, 0, 1, 0, -1, 1, 1, -1, 0, 1, -1, 0, 2, -1, -1, 2, -1, -2, 3, 1, -3, 2, 1, -4, 2, 3, -4, 1, 4, -5, 0, 6, -5, -2, 7, -5, -4, 10, -3, -7, 10, -2, -10, 11, 1, -13, 11, 4, -16, 11, 9, -19, 8, 12, -22, 7, 19, -24, 2, 24, -26, -3, 32, -25, -10, 37, -25, -18, 45, -21, -29, 49, -17, -39, 56, -8, -51, 58, 0, -65, 61, 14, -78, 59, 27, -92
(list; graph; listen)
|
|
|
OFFSET
|
0,15
|
|
|
REFERENCES
|
G. E. Andrews and B. C. Berndt, Your Hit Parade: The Top Ten Most Fascinating Formulas in Ramanujan's Lost Notebook, Notices Amer. Math. Soc., 55 (No. 1, 2008), 18-30. See p. 25, Equation (39).
|
|
FORMULA
|
Euler transform of period 3 sequence [ 1, -1, 0, ...]. - Michael Somos Dec 23 2007
G.f.: Product_{k>=0} (1 - x^(3*k+2)) / (1 - x^(3*k+1)).
|
|
PROGRAM
|
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=0, n\3, (1 - x^(3*k+2)) / (1 - x^(3*k+1)), 1 + x * O(x^n)), n))} /* Michael Somos Dec 23 2007 */
|
|
CROSSREFS
|
Convolution inverse of A111165.
Sequence in context: A050205 A137900 A025837 this_sequence A105202 A099386 A161067
Adjacent sequences: A111314 A111315 A111316 this_sequence A111318 A111319 A111320
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Nov 09 2005
|
|
|
Search completed in 0.002 seconds
|
