|
| |
|
|
A132320
|
|
Expansion of q^-1 * (chi(-q) * chi(-q^11))^2 in powers of q where chi() is a Ramanujan theta function.
|
|
0
|
|
|
|
1, -2, 1, -2, 4, -4, 5, -6, 9, -12, 13, -18, 25, -28, 33, -44, 54, -64, 74, -92, 114, -132, 155, -186, 224, -260, 303, -360, 424, -488, 565, -662, 770, -888, 1018, -1180, 1366, -1560, 1780, -2048, 2345, -2668, 3034, -3460, 3946, -4468, 5052, -5734, 6502, -7328, 8255, -9320, 10512, -11808
(list;
graph;
refs;
listen;
history;
text;
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).
|
|
|
LINKS
|
Table of n, a(n) for n=-1..52.
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
|
Expansion of (eta(q) * eta(q^11)/( eta(q^2) * eta(q^22)))^2 in powers of q.
Euler transform of period 22 sequence [ -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, -4, 0, -2, 0, -2, 0, -2, 0, -2, 0, -2, 0, ...].
G.f. is a Fourier series which satisfies f(-1 / (22 t)) = 4 / f(t) where q = exp(2 pi i t).
G.f.: x^-1 * (Product_{k>0} (1+x^k) * (1+x^(11*k)))^-2.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 * v - v^2 + 4 * u + 4 * u * v.
|
|
|
EXAMPLE
|
q^-1 - 2 + q - 2*q^2 + 4*q^3 - 4*q^4 + 5*q^5 - 6*q^6 + 9*q^7 - ...
|
|
|
PROG
|
(PARI) {a(n) = local(A); if(n<-1, 0, n++; A = x*O(x^n); polcoeff( (eta(x+A) * eta(x^11+A) / eta(x^2+A) / eta(x^22+A))^2, n))}
|
|
|
CROSSREFS
|
A058568(n) = a(n) unless n = 0.
Sequence in context: A022597 A073252 A134005 * A076369 A072727 A057061
Adjacent sequences: A132317 A132318 A132319 * A132321 A132322 A132323
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Michael Somos, Aug 18 2007
|
|
|
STATUS
|
approved
|
| |
|
|
