A058497 McKay-Thompson series of class 14A for Monster.

1, 0, 11, 20, 57, 92, 207, 312, 623, 932, 1674, 2464, 4162, 6024, 9595, 13748, 21126, 29820, 44449, 62004, 90191, 124288, 177135, 241632, 338508, 457272, 631031, 845008, 1150752, 1528380, 2057700, 2712192, 3614217, 4730148, 6245541, 8119672

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

a(n) ~ exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of A - 4 + 1/A, where A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14) ))^4, in powers of q. - G. C. Greubel, Jun 18 2018

Example

T14A = 1/q + 11*q + 20*q^2 + 57*q^3 + 92*q^4 + 207*q^5 + 312*q^6 + 623*q^7 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; e14C := (eta[q^2]*eta[q^7]/(eta[q] *eta[q^14]))^4; a:= CoefficientList[Series[-4 + e14C + 1/e14C, {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^7)/(eta(q)*eta(q^14) ))^4/q; Vec(A - 4 + 1/A) \\ G. C. Greubel, Jun 18 2018

Crossrefs

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

Cf. A134782 (same sequence except for n=0).

Sequence in context: A158245 A076851 A164576 * A134782 A067969 A068599

Adjacent sequences: A058494 A058495 A058496 * A058498 A058499 A058500

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 19 2014

Status

approved