|
Search: id:A128633
|
|
|
| A128633 |
|
Expansion of 3* (b(q^2)^2/ b(q))/ (c(q^2)^2/ c(q)) in powers of q where b(), c() are cubic AGM analog functions. |
|
+0
3
|
|
| 1, 4, 6, 4, -3, -12, -8, 12, 30, 20, -30, -72, -46, 60, 156, 96, -117, -300, -188, 228, 552, 344, -420, -1008, -603, 732, 1770, 1048, -1245, -2976, -1776, 2088, 4908, 2900, -3420, -7992, -4658, 5460, 12756, 7408, -8583, -19944, -11564, 13344, 30756, 17744, -20448, -46944
(list; graph; listen)
|
|
|
OFFSET
|
-1,2
|
|
|
COMMENT
|
McKay-Thompson series of class 6E for the Monster group with a(0) = 4.
|
|
FORMULA
|
Expansion of q^-1* (psi(q)/ psi(q^3))^4 in powers of q where psi() is a Ramanujan theta function.
Expansion of (eta(q^2)^2* eta(q^3)/( eta(q)* eta(q^6)^2))^4 in powersof q.
Euler transform of period 6 sequence [ 4, -4, 0, -4, 4, 0, ...].
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= v* (u-9)* (u-1) -(u-v)^2.
G.f.: (1/x)* (Product_{k>0} (1 +x^k +x^(2k))* (1 -x^k +x^(2k))^2)^-4.
Expansion of 3 * (b(q^2)^2 / b(q)) / (c(q^2)^2 / c(q)) in powers of q where b(), c() are cubic AGM functions.
|
|
EXAMPLE
|
1/q + 4 + 6*q + 4*q^2 - 3*q^3 - 12*q^4 - 8*q^5 + 12*q^6 + 30*q^7 + ...
|
|
PROGRAM
|
(PARI) {a(n)= local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff( (eta(x^2+A)^2* eta(x^3+A)/ eta(x+A)/ eta(x^6+A)^2)^4, n))}
|
|
CROSSREFS
|
A007258(n) = A105559(n) = A128632(n) = a(n) unless n = 0.
Sequence in context: A135911 A001138 A133587 this_sequence A001482 A078385 A137429
Adjacent sequences: A128630 A128631 A128632 this_sequence A128634 A128635 A128636
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Mar 15 2007
|
|
|
Search completed in 0.002 seconds
|
