A062245 Expansion of Hauptmodul for group G'_{27|3}.

1, 1, -1, 0, 0, -1, 0, -1, 0, -1, -1, 1, -1, 0, 1, 1, 1, 0, 2, 2, -2, 1, 1, -2, -1, -2, 1, -3, -3, 3, -2, -1, 3, 2, 3, 0, 5, 5, -5, 3, 1, -5, -3, -5, 1, -7, -7, 7, -5, -2, 7, 4, 7, -1, 11, 11, -11, 6, 3, -11, -6, -11, 2, -15, -15, 15, -10, -4, 15, 9, 14, -2, 22, 22, -22, 13, 6, -21, -12, -21, 4, -30, -30, 30, -19, -8, 29, 17, 28, -4, 42

Offset

0,19

Links

Table of n, a(n) for n=0..90.

J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.

Formula

Expansion of q^(1/3) * eta(q^2)^3 * eta(q^9) * eta(q^36) / (eta(q) * eta(q^12) * eta(q^18)^3) in powers of q.

Euler transform of period 36 sequence [ 1, -2, 1, -1, 1, -2, 1, -1, 0, -2, 1, -1, 1, -2, 1, -1, 1, 0, 1, -1, 1, -2, 1, -1, 1, -2, 0, -1, 1, -2, 1, -1, 1, -2, 1, 0, ...].

a(n) = (-1)^n * A062246(n).

Example

G.f. = 1 + x - x^2 - x^5 - x^7 - x^9 - x^10 + x^11 - x^12 + x^14 + x^15 + x^16 + ...
G.f. = 1/q + q^2 - q^5 - q^14 - q^20 - q^26 - q^29 + q^32 - q^35 + q^41 + q^44 + ...

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(-x + A) / eta(-x^9 + A), n))}; /* Michael Somos, Jun 26 2004 */

Crossrefs

Cf. A007706, A062246.

Sequence in context: A108393 A327342 A297828 * A062246 A034095 A037811

Adjacent sequences: A062242 A062243 A062244 * A062246 A062247 A062248

Keyword

sign,easy

Author

N. J. A. Sloane, Jul 01 2001

Status

approved