|
| |
|
|
A134178
|
|
Expansion of chi(q) * chi(-q^2)^2 * chi(-q^4) * chi(q^6) * chi(-q^12)^2 / chi(-q^3) in powers of q where chi() is a Ramanujan theta function.
|
|
0
| |
|
|
1, 1, -2, -2, 0, 1, 2, 0, 0, -1, -4, 0, 1, 0, 6, 2, 0, 1, -8, 0, 0, 0, 12, 0, -1, -1, -18, -4, 0, -1, 24, 0, 0, 2, -32, 0, 0, 1, 44, 6, 0, -2, -58, 0, 0, -1, 76, 0, 1, 2, -100, -8, 0, 1, 128, 0, 0, -3, -164, 0, 0, -1, 210, 12, 0, 4, -264, 0, 0, 2, 332, 0, -1, -5, -416, -18, 0, -2, 516, 0, 0, 5, -640, 0, -1, 2, 790, 24
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
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
| Euler transform of period 24 sequence [ 1, -3, 0, -1, 1, -1, 1, 0, 0, -3, 1, -4, 1, -3, 0, 0, 1, -1, 1, -1, 0, -3, 1, 0, ...].
a(12*n+4) = a(12*n+7) = a(12*n+8) = a(12*n+11) = 0.
|
|
|
EXAMPLE
| q^-3 + q^-1 - 2*q - 2*q^3 + q^7 + 2*q^9 - q^15 - 4*q^17 + q^21 + 6*q^25 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^12 + A)^5/ (eta(x + A) * eta(x^4 + A)^2 * eta(x^6 + A)^3 * eta(x^8 + A) * eta(x^24 + A)^3), n))}
|
|
|
CROSSREFS
| A029838(n) = a(4*n+1) = a(12*n). -2 * A083365(n) = a(4*n+2) = a(12*n+3).
Sequence in context: A104579 A079531 A182882 * A059018 A122190 A146093
Adjacent sequences: A134175 A134176 A134177 * A134179 A134180 A134181
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Michael Somos, Oct 11 2007
|
| |
|
|
