A058587 McKay-Thompson series of class 24d for Monster.

1, -1, 3, 3, 6, -3, 10, 1, 15, 0, 24, 3, 37, -9, 57, 12, 84, -12, 118, 9, 165, -6, 228, 12, 316, -27, 432, 42, 582, -42, 776, 28, 1023, -24, 1344, 45, 1757, -82, 2283, 111, 2946, -111, 3774, 91, 4812, -84, 6108, 123, 7725, -208, 9732, 279, 12204, -282, 15240, 234, 18957, -222, 23508, 321, 29065, -495, 35826, 630, 44022, -642

Offset

0,3

Comments

This sequence is A112163 with alternating signs: T24d(q) = i*T24e(i*q). - G. A. Edgar, Mar 13 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..149 from G. A. Edgar)

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

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of q^(1/2)*(eta(q^4)^3*eta(q^6)^3 / (eta(q^2)^3*eta(q^12)^3) - eta(q^2)^3*eta(q^12)^3 / (eta(q^4)^3*eta(q^6)^3)) in powers of q. - G. A. Edgar, Mar 13 2017

Example

T24d = 1/q - q + 3*q^3 + 3*q^5 + 6*q^7 - 3*q^9 + 10*q^11 + q^13 + 15*q^15 + ...

Mathematica

CoefficientList[Series[(QPochhammer[x^4]^3*QPochhammer[x^6]^3 / (QPochhammer[x^2]^3 * QPochhammer[x^12]^3) - x * QPochhammer[x^2]^3 * QPochhammer[x^12]^3 / (QPochhammer[x^4]^3 * QPochhammer[x^6]^3)), {x, 0, 66}], x] (* Indranil Ghosh, Mar 14 2017 *)

Prog

(PARI) q='q+O('q^66); Vec( (eta(q^4)^3*eta(q^6)^3 / (eta(q^2)^3*eta(q^12)^3) - q*eta(q^2)^3*eta(q^12)^3 / (eta(q^4)^3*eta(q^6)^3)) ) \\ Joerg Arndt, Mar 13 2017

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A308083 A181788 A112163 * A196439 A184389 A163163

Adjacent sequences: A058584 A058585 A058586 * A058588 A058589 A058590

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from G. A. Edgar, Mar 13 2017

Status

approved