|
| |
|
|
A145785
|
|
Expansion of q * f(-q^2) * f(-q^30) / (f(q^3) * f(q^5)) in powers of q where f() is a Ramanujan theta function.
|
|
1
| |
|
|
1, 0, -1, -1, -1, 0, 2, 2, -1, -2, 0, 1, 2, 2, -3, -7, -2, 6, 8, 5, -2, -12, -10, 6, 13, 4, -7, -14, -10, 14, 32, 12, -24, -36, -22, 13, 50, 36, -26, -56, -22, 30, 62, 40, -51, -114, -46, 79, 129, 76, -54, -170, -114, 90, 192, 82, -104, -216, -132, 159, 350, 152, -230, -397, -226, 180, 506, 322, -270, -574, -260
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,7
|
|
|
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) * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30) / (eta(q^6) * eta(q^10))^3 in powers of q.
Euler transform of period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).
|
|
|
EXAMPLE
| q - q^3 - q^4 - q^5 + 2*q^7 + 2*q^8 - q^9 - 2*q^10 + q^12 + 2*q^13 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A) / (eta(x^6 + A) * eta(x^10 + A))^3, n))}
|
|
|
CROSSREFS
| Convolution inverse of A058727. -(-1)^n * A094022(n) = a(n).
Sequence in context: A144191 A145783 A094022 * A128580 A129402 A134177
Adjacent sequences: A145782 A145783 A145784 * A145786 A145787 A145788
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Michael Somos, Oct 23 2008
|
| |
|
|
