A058625 McKay-Thompson series of class 30d for Monster.

1, 2, 2, 7, 5, 11, 21, 24, 31, 49, 57, 85, 114, 144, 179, 251, 306, 390, 511, 619, 772, 1008, 1203, 1498, 1862, 2255, 2757, 3407, 4067, 4927, 6005, 7180, 8581, 10395, 12266, 14652, 17542, 20673, 24452, 29057, 34058, 40172, 47332, 55341, 64719, 75999, 88401, 103051, 120225, 139348

Offset

0,2

Comments

The convolution square of this sequence is A153765: T30d(q)^2 = T15A(q^2). - G. A. Edgar, Mar 18 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..500 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

a(n) ~ exp(2*Pi*sqrt(2*n/15))/ (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 18 2017

Expansion of A + 3*q/A, where A = q^(1/2)*eta(q)*eta(q^5)/(eta(q^3)* eta(q^15)), in powers of q. - G. C. Greubel, Jun 14 2018

Example

T30d = 1/q + 2*q + 2*q^3 + 7*q^5 + 5*q^7 + 11*q^9 + 21*q^11 + 24*q^13 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*eta[q]*eta[q^5]/(eta[q^3]* eta[q^15]);  a:= CoefficientList[Series[A + 3*q/A, {q, 0, 60}], q]; Table[A058625[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q)*eta(q^5)/(eta(q^3)*eta(q^15)); Vec(A + 3*q/A) \\ G. C. Greubel, Jun 14 2018

Crossrefs

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

Sequence in context: A197735 A249493 A223000 * A300126 A006748 A193548

Adjacent sequences: A058622 A058623 A058624 * A058626 A058627 A058628

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Status

approved