|
Search: id:A132977
|
|
|
| A132977 |
|
Expansion of q^(-1/3) * (eta(q^6)^4 / (eta(q) * eta(q^3) * eta(q^4) * eta(q^12)))^2 in powers of q. |
|
+0
1
|
|
| 1, 2, 5, 12, 26, 50, 92, 168, 295, 496, 818, 1332, 2126, 3324, 5126, 7824, 11793, 17548, 25857, 37788, 54734, 78578, 111968, 158496, 222842, 311224, 432095, 596676, 819504, 1119624, 1522282, 2060448, 2776514, 3725294, 4978142, 6626988, 8789042
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
Expansion of q^(-2/3) * (chi(q) * chi(q^3))^2 * c(q^2) / (3 * b(q^2)) in powers of q where chi() is a Ramanujan theta function and b(), c() are cubic AGM functions.
Euler transform of period 12 sequence [ 2, 2, 4, 4, 2, -4, 2, 4, 4, 2, 2, 0, ...].
G.f. = A112173(x) * A128758(x^2).
G.f.: (Product_{k>0} (1-x^(6*k))^4 / ( (1-x^k) * (1-x^(3*k)) * (1-x^(4*k)) * (1-x^(12*k)) ))^2.
|
|
EXAMPLE
|
q + 2*q^4 + 5*q^7 + 12*q^10 + 26*q^13 + 50*q^16 + 92*q^19 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x^6 + A)^4 / eta(x + A) / eta(x^3 + A) / eta(x^4 + A) / eta(x^12 + A))^2, n))}
|
|
CROSSREFS
|
A132975(3*n+1) = a(n).
Sequence in context: A063807 A116715 A117177 this_sequence A027927 A116717 A116725
Adjacent sequences: A132974 A132975 A132976 this_sequence A132978 A132979 A132980
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Sep 07 2007
|
|
|
Search completed in 0.002 seconds
|
