A058753 McKay-Thompson series of class 76a for Monster.

1, 0, 1, 1, 2, 1, 2, 1, 3, 3, 4, 3, 6, 4, 7, 6, 10, 8, 12, 11, 16, 14, 20, 18, 26, 23, 31, 30, 40, 37, 49, 46, 60, 58, 73, 71, 90, 87, 109, 107, 133, 130, 160, 157, 192, 190, 229, 229, 275, 274, 326, 328, 388, 390, 459, 463, 542, 550, 638, 649, 752, 764, 880, 899, 1031, 1054, 1204

Offset

-1,5

Links

G. C. Greubel, Table of n, a(n) for n = -1..1500

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

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of sqrt(T38A), where T38A = A058657, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(n/19)) / (2 * 19^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

Example

T76a = 1/q + q^3 + q^5 + 2*q^7 + q^9 + 2*q^11 + q^13 + 3*q^15 + 3*q^17 + ...

Mathematica

nmax = 100; QP := QPochhammer; G[q_] := 1/(QP[q, q^5]*QP[q^4, q^5]); H[q_] := 1/(QP[q^2, q^5]*QP[q^3, q^5]); T19A := -3 + (G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q; T38A := -1/2 + (17/4 + T19A + (T19A /. {q -> q^2}) + O[q]^nmax)^(1/2);  a:= CoefficientList[Series[(q*T38A + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

Crossrefs

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

Sequence in context: A030273 A029197 A029174 * A282249 A330953 A360308

Adjacent sequences: A058750 A058751 A058752 * A058754 A058755 A058756

Keyword

nonn,more

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 24 2018

Status

approved