A058739 McKay-Thompson series of class 66A for Monster.

1, 0, 2, 0, 1, 2, 2, 2, 4, 2, 5, 6, 7, 6, 12, 8, 13, 14, 19, 16, 25, 20, 31, 32, 40, 38, 55, 48, 64, 68, 83, 80, 108, 102, 130, 136, 163, 162, 209, 200, 247, 260, 306, 308, 383, 378, 455, 478, 553, 566, 683, 686, 805, 848, 972, 1004, 1183, 1204, 1395, 1468

Offset

-1,3

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 A - 1 + 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

T66A = 1/q + 2*q + q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 4*q^7 + 2*q^8 + 5*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 + 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(A - 1 + 1/A) \\ G. C. Greubel, Jun 29 2018

Crossrefs

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

Sequence in context: A254212 A033773 A029275 * A128627 A105422 A166291

Adjacent sequences: A058736 A058737 A058738 * A058740 A058741 A058742

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved