|
Search: id:A139136
|
|
|
| A139136 |
|
Expansion of psi(-q) / f(q^3) where psi(), f() are Ramanujan theta functions. |
|
+0
2
|
|
| 1, -1, 0, -2, 1, 0, 4, -2, 0, -6, 4, 0, 10, -6, 0, -16, 9, 0, 24, -14, 0, -36, 20, 0, 52, -29, 0, -74, 42, 0, 104, -58, 0, -144, 80, 0, 198, -110, 0, -268, 148, 0, 360, -198, 0, -480, 264, 0, 634, -347, 0, -832, 454, 0, 1084, -592, 0, -1404, 764, 0, 1808, -982, 0, -2316, 1257, 0, 2952, -1598, 0, -3744
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
Expansion of eta(q) * eta(q^3) * eta(q^4) * eta(q^12) / (eta(q^2) * eta(q^6)^3) in powers of q.
Euler transform of period 12 sequence [ -1, 0, -2, -1, -1, 2, -1, -1, -2, 0, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 3^(-1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A139135.
a(3*n + 2) = 0.
G.f.: Product_{k>0} P(12, x^k) / ( (1 + x^(2*k-1))^2 * P(3, x^k) * P(6, x^k)^2) where P(n, x) is nth cyclotomic polynomial.
|
|
EXAMPLE
|
1 - q - 2*q^3 + q^4 + 4*q^6 - 2*q^7 - 6*q^9 + 4*q^10 + 10*q^12 - 6*q^13 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A) / (eta(x^2 + A) * eta(x^6 + A)^3), n))}
|
|
CROSSREFS
|
A132002(n) = a(3*n). - A139135(n) = a(3*n + 1).
Sequence in context: A122073 A106236 A122792 this_sequence A138002 A062296 A091453
Adjacent sequences: A139133 A139134 A139135 this_sequence A139137 A139138 A139139
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Apr 10 2008
|
|
|
Search completed in 0.002 seconds
|
