A058535 McKay-Thompson series of class 18E for Monster.

1, 0, 6, 13, 24, 42, 73, 120, 192, 299, 456, 684, 1007, 1464, 2100, 2976, 4176, 5802, 7993, 10920, 14808, 19946, 26688, 35496, 46944, 61752, 80826, 105286, 136536, 176304, 226725, 290448, 370704, 471467, 597600, 755028, 950980, 1194216

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).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of A + 2 + 6/A, where A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2) *eta(q^3)*eta(q^18)^2)), in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

Example

T18E = 1/q + 6*q + 13*q^2 + 24*q^3 + 42*q^4 + 73*q^5 + 120*q^6 + 192*q^7 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; e18D3:= (eta[q]^2*eta[q^6]*eta[q^9]/( eta[q^2]*eta[q^3]*eta[q^18]^2)); a := CoefficientList[Series[2 + e18D3 + 6/e18D3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2)*eta(q^3) *eta(q^18)^2))/q; Vec(A + 2 + 6/A) \\ G. C. Greubel, Jun 18 2018

Crossrefs

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

Cf. A128517 (same sequence except for n=0).

Sequence in context: A296310 A235450 A032528 * A131833 A101736 A162432

Adjacent sequences: A058532 A058533 A058534 * A058536 A058537 A058538

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 19 2014

Status

approved