|
Search: id:A132002
|
|
|
| A132002 |
|
Expansion of phi(q^3)/phi(q) in powers of q where phi() is a Ramanujan theta function. |
|
+0
3
|
|
| 1, -2, 4, -6, 10, -16, 24, -36, 52, -74, 104, -144, 198, -268, 360, -480, 634, -832, 1084, -1404, 1808, -2316, 2952, -3744, 4728, -5946, 7448, -9294, 11556, -14320, 17688, -21780, 26740, -32736, 39968, -48672, 59122, -71644, 86616, -104484, 125768, -151072, 181104, -216684
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
Expansion of eta(q)^2* eta(q^4)^2* eta(q^6)^5/( eta(q^2)^5* eta(q^3)^2* eta(q^12)^2) in powers of q.
Euler transform of period 12 sequence [ -2, 3, 0, 1, -2, 0, -2, 1, 0, 3, -2, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= (v+u)* (v-u) +(1 -u*v)* (1 -3*u*v).
G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= u^3 -v +3*u*v^2* (1-u*v).
G.f.: (Sum_k x^(3k^2))/(Sum_k x^k^2) = Product_{k>0} (1+x^k+x^(2k))* (1-x^k+x^(2k))^3/ (1-x^(2k)+x^(4k))^2.
|
|
PROGRAM
|
(PARI) {a(n)= if(n<0, 0, polcoeff( sum(k=1, sqrtint(n\3), 2*x^(3*k^2), 1+x*O(x^n))/ sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n)), n))}
(PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x+A)^2* eta(x^4+A)^2* eta(x^6+A)^5/ eta(x^2+A)^5/ eta(x^3+A)^2/ eta(x^12+A)^2, n))}
|
|
CROSSREFS
|
a(n)= (-1)^n* A098151(n).
Sequence in context: A132212 A137414 A098151 this_sequence A028445 A006305 A067247
Adjacent sequences: A131999 A132000 A132001 this_sequence A132003 A132004 A132005
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Aug 06 2007
|
|
|
Search completed in 0.002 seconds
|
