A058637 McKay-Thompson series of class 33B for Monster.

1, 0, 2, 4, 5, 6, 14, 14, 20, 30, 37, 46, 71, 82, 108, 144, 173, 218, 291, 340, 425, 540, 647, 788, 996, 1170, 1427, 1744, 2072, 2476, 3019, 3536, 4224, 5058, 5942, 7008, 8363, 9734, 11453, 13512, 15719, 18340, 21546, 24908, 28983, 33774, 38995, 45086, 52353

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 + 3/A, where A =eta(q)*eta(q^11)/(eta(q^3)*eta(q^33)), in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ exp(4*Pi*sqrt(n/33)) / (sqrt(2) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T33B = 1/q + 2*q + 4*q^2 + 5*q^3 + 6*q^4 + 14*q^5 + 14*q^6 + 20*q^7 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := eta[q]*eta[q^11]/( eta[q^3]* eta[q^33]); a:= CoefficientList[Series[q*(A + 1 + 3/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(A + 1 + 3/A) \\ G. C. Greubel, Jun 23 2018

Crossrefs

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

Sequence in context: A191165 A360994 A324778 * A026473 A272929 A336129

Adjacent sequences: A058634 A058635 A058636 * A058638 A058639 A058640

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved