|
Search: id:A123532
|
|
|
| A123532 |
|
Expansion of (eta(q)*eta(q^6))^7/(eta(q^2)*eta(q^3))^5 in powers of q. |
|
+0
1
|
|
| 1, -7, 19, -23, 6, 11, 8, -55, 73, -42, 12, -5, 14, -56, 114, -119, 18, 65, 20, -138, 152, -84, 24, -37, 31, -98, 235, -184, 30, 66, 32, -247, 228, -126, 48, 49, 38, -140, 266, -330, 42, 88, 44, -276, 438, -168, 48, -101, 57, -217, 342, -322, 54, 227, 72, -440, 380, -210, 60, -30, 62, -224
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
FORMULA
|
Euler transform of period 6 sequence [ -7, -2, -2, -2, -7, -4, ...].
Expansion of q*phi(-q)^3*psi(q^3)^3/(phi(-q^3)*psi(q)) in powers of q where phi(),psi() are Ramanujan theta functions.
Expansion of (b(q)^2/b(q^2))(c(q^2)^2/c(q))/3 in powers of q where b(),c() are cubic AGM analog functions.
G.f.: x*Product_{k>0} (1-x^k)^2*(1-x^(3k))^2*(1+x^(3k))^7/(1+x^k)^5.
|
|
PROGRAM
|
(PARI) {a(n)=if(n<1, 0, sumdiv(n, d, d*[0, 1, -4, 6, -4, 1][d%6+1]))}
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x+A)*eta(x^6+A))^7/(eta(x^2+A)*eta(x^3+A))^5, n))}
|
|
CROSSREFS
|
Adjacent sequences: A123529 A123530 A123531 this_sequence A123533 A123534 A123535
Sequence in context: A109637 A039513 A125265 this_sequence A113972 A082422 A129812
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Oct 02 2006
|
|
|
Search completed in 0.002 seconds
|
