A058567 McKay-Thompson series of class 22A for Monster.

1, 0, 5, 6, 16, 20, 41, 50, 97, 116, 197, 246, 397, 492, 753, 932, 1378, 1712, 2434, 3028, 4210, 5204, 7075, 8750, 11692, 14396, 18943, 23256, 30220, 36968, 47477, 57890, 73614, 89448, 112726, 136564, 170734, 206136, 255872, 308000, 379801, 455828, 558714

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 + 2 + 4/A, where A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22) ))^2, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(3/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T22A = 1/q + 5*q + 6*q^2 + 16*q^3 + 20*q^4 + 41*q^5 + 50*q^6 + 97*q^7 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^11]/(eta[q^2]* eta[q^22]))^2;  a:= CoefficientList[Series[q*(2 + A + 4/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A + 2 + 4/A) \\ G. C. Greubel, Jun 21 2018

Crossrefs

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

Sequence in context: A104422 A026547 A081283 * A115376 A076650 A068408

Adjacent sequences: A058564 A058565 A058566 * A058568 A058569 A058570

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved