|
Search: id:A137677
|
|
|
| A137677 |
|
Expansion of f(-q^2) * f(-q^5) / ( f(-q^4) * f(-q^2, -q^3) ) in powers of q where f(,) is Ramanujan's two-variable theta function. |
|
+0
1
|
|
| 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 3, 4, 0, 0, 4, 4, 0, 0, 5, 6, 0, 0, 7, 7, 0, 0, 9, 10, 0, 0, 11, 11, 0, 0, 14, 16, 0, 0, 18, 18, 0, 0, 22, 24, 0, 0, 27, 28, 0, 0, 34, 36, 0, 0, 41, 42, 0, 0, 50, 54, 0, 0, 61, 62, 0, 0, 73, 78, 0, 0, 88, 91, 0, 0, 106, 112, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,16
|
|
|
REFERENCES
|
G. E. Andrews, q-series, CBMS Regional Conference Series in Mathematics, 66, Amer. Math. Soc. 1986, see p. 36, Eq. (4.12). MR0858826 (88b:11063)
|
|
FORMULA
|
Expansion of ( f(-q^11, -q^19) + q^3 * f(-q, -q^29) ) / f(-q^4) in powers of q where f(,) is Ramanujan's two-variable theta function.
Euler transform of period 20 sequence [ 0, 0, 1, 0, 0, -1, 1, 1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, 0, ...].
a(4*n+1) = a(4*n+2) = 0.
|
|
PROGRAM
|
(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, sqrtint(n+1)-1, x^(k^2+2*k) / prod(i=1, k, 1 - x^(4*i), 1 + x*O(x^(n-k^2-2*k)))), n))}
|
|
CROSSREFS
|
A122134(n) = a(4*n). A122130(n) = a(4*n+3).
Sequence in context: A134015 A033461 A143432 this_sequence A015818 A039972 A031124
Adjacent sequences: A137674 A137675 A137676 this_sequence A137678 A137679 A137680
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Feb 04 2008
|
|
|
Search completed in 0.002 seconds
|
