A062246 McKay-Thompson series of class 27c for the Monster group.

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

Seiichi Manyama, Table of n, a(n) for n = 0..10000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

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

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of q^(1/3) * eta(q) / eta(q^9) in powers of q.

Euler transform of period 9 sequence [ -1, -1, -1, -1, -1, -1, -1, -1, 0, ...].

a(n) = (-1)^n * A062245(n).

a(n) = -(1/n)*Sum_{k=1..n} A116607(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 25 2017

Example

1 - x - x^2 + x^5 + x^7 + x^9 - x^10 - x^11 - x^12 + x^14 - x^15 + x^16 + ...
T27c = 1/q - q^2 - q^5 + q^14 + q^20 + q^26 - q^29 - q^32 - q^35 + q^41 - ...

Mathematica

QP = QPochhammer; s = QP[q]/QP[q^9] + O[q]^90; CoefficientList[s, q] (* Jean-François Alcover, Nov 12 2015 *)

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, A062245.

Sequence in context: A327342 A297828 A062245 * A034095 A037811 A091237

Adjacent sequences: A062243 A062244 A062245 * A062247 A062248 A062249

Keyword

sign

Author

N. J. A. Sloane, Jul 01 2001

Extensions

Additional comments from Michael Somos, Jun 28 2004

Status

approved