|
| |
|
|
A164613
|
|
Expansion of (phi(q) / phi(q^9))^2 in powers of q where phi() is a Ramanujan theta function.
|
|
1
| |
|
|
1, 4, 4, 0, 4, 8, 0, 0, 4, 0, -8, -16, 0, -8, -32, 0, 4, -8, 0, 16, 56, 0, 16, 96, 0, -4, 24, 0, -32, -152, 0, -32, -252, 0, 8, -64, 0, 56, 368, 0, 56, 600, 0, -16, 144, 0, -96, -832, 0, -92, -1316, 0, 24, -312, 0, 160, 1760, 0, 152, 2736, 0, -40, 640, 0, -252, -3536, 0, -240, -5432, 0, 64, -1248, 0, 392
(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 (eta(q^2)^5 * eta(q^9)^2 * eta(q^36)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^18)^5))^2 in powers of q.
a(3*n) = 0 unless n=0. a(3*n + 1) = 4 * A128111(n). a(3*n + 2) = 4 * A164614(n).
Euler transform of period 36 sequence [ 4, -6, 4, -2, 4, -6, 4, -2, 0, -6, 4, -2, 4, -6, 4, -2, 4, 0, 4, -2, 4, -6, 4, -2, 4, -6, 0, -2, 4, -6, 4, -2, 4, -6, 4, 0, ...].
Convolution square of A139380.
|
|
|
EXAMPLE
| 1 + 4*q + 4*q^2 + 4*q^4 + 8*q^5 + 4*q^8 - 8*q^10 - 16*q^11 - 8*q^13 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^5 * eta(x^9 + A)^2 * eta(x^36 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^18 + A)^5))^2, n))}
|
|
|
CROSSREFS
| Sequence in context: A174611 A138518 A155836 * A104794 A004018 A028658
Adjacent sequences: A164610 A164611 A164612 * A164614 A164615 A164616
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Michael Somos, Aug 17 2009
|
| |
|
|
