|
| |
|
|
A132218
|
|
Expansion of psi(-q^3)/ phi(-q) in powers of q where psi(), phi() are Ramanujan theta functions.
|
|
0
| |
|
|
1, 2, 4, 7, 12, 20, 32, 50, 76, 113, 166, 240, 342, 482, 672, 928, 1270, 1724, 2323, 3108, 4132, 5460, 7174, 9376, 12192, 15780, 20332, 26086, 33334, 42432, 53817, 68018, 85680, 107584, 134674, 168092, 209210, 259680, 321484, 396996, 489056, 601052
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
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).
|
|
|
LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
| Expansion of q^(-3/8)* eta(q^2)* eta(q^3)* eta(q^12)/( eta(q)^2* eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, ...].
G.f.: Product_{k>0} (1+x^k)* (1+x^k+x^(2*k))* (1+x^(6*k)).
|
|
|
PROG
| (PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( eta(x^2+A)* eta(x^3+A)* eta(x^12+A)/ eta(x+A)^2/ eta(x^6+A), n))}
|
|
|
CROSSREFS
| Sequence in context: A122515 A193840 A036372 * A101230 A128129 A014968
Adjacent sequences: A132215 A132216 A132217 * A132219 A132220 A132221
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Michael Somos, Aug 13 2007
|
| |
|
|
