|
| |
|
|
A123653
|
|
Expansion of (eta(q^2)eta(q^6)/(eta(q)eta(q^3)))^6 in powers of q.
|
|
2
| |
|
|
1, 6, 21, 68, 198, 510, 1248, 2904, 6393, 13604, 28044, 55956, 108982, 207552, 386622, 707216, 1271970, 2250582, 3925780, 6757272, 11483232, 19290824, 32057352, 52722744, 85884503, 138644292, 221885805, 352241792, 554892894
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
Expansion of q/(chi(-q)*chi(-q^3))^6 in powers of q where chi() is a Ramanujan theta function.
|
|
|
LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
| Euler transform of period 6 sequence [ 6, 0, 12, 0, 6, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v*(1+12*u+64*u*v)
G.f.: x*(Product_{k>0} (1+x^k)*(1+x^(3k)))^6.
|
|
|
PROG
| (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^6+A)/eta(x+A)/eta(x^3+A))^6, n))}
|
|
|
CROSSREFS
| Sequence in context: A119103 A180795 A107653 * A200761 A169687 A101904
Adjacent sequences: A123650 A123651 A123652 * A123654 A123655 A123656
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Michael Somos, Oct 04 2006
|
| |
|
|
