A058740 McKay-Thompson series of class 66B for Monster.

1, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 6, 7, 8, 9, 10, 12, 14, 17, 19, 21, 24, 29, 33, 38, 43, 48, 54, 61, 70, 79, 88, 98, 111, 124, 140, 157, 174, 193, 214, 239, 266, 295, 326, 361, 398, 441, 488, 538, 592, 650, 715, 786, 864, 948, 1041, 1138, 1246, 1364, 1492

Offset

-1,6

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of -1 + A, where A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( eta(q)*eta(q^6)*eta(q^11)*eta(q^66)), in powers of q. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(2*Pi*sqrt(2*n/33)) / (2^(3/4) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T66B = 1/q + q + q^2 + q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 3*q^7 + 3*q^8 + 4*q^9 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^3]*eta[q^22]* eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]);  a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( q*eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); Vec(-1 + A) \\ G. C. Greubel, Jun 29 2018

Crossrefs

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

Sequence in context: A227396 A331590 A326496 * A160642 A110868 A110869

Adjacent sequences: A058737 A058738 A058739 * A058741 A058742 A058743

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved