A058596 McKay-Thompson series of class 26A for Monster.

1, 0, 4, 4, 10, 12, 26, 28, 51, 60, 102, 116, 189, 220, 336, 396, 575, 684, 974, 1152, 1588, 1892, 2554, 3032, 4017, 4780, 6234, 7404, 9519, 11292, 14368, 17012, 21402, 25308, 31552, 37228, 46039, 54216, 66566, 78232, 95384, 111892, 135624, 158764, 191359

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 + 1/A, where A = (eta(q^2)*eta(q^13)/(eta(q)* eta(q^26)))^2, in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(2*Pi*sqrt(2*n/13)) / (2^(3/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T26A = 1/q + 4*q + 4*q^2 + 10*q^3 + 12*q^4 + 26*q^5 + 28*q^6 + 51*q^7 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^13]/(eta[q]* eta[q^26]))^2; a:= CoefficientList[Series[-2 + e26B + 1/e26B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^13)/(eta(q)*eta(q^26)))^2/q; Vec(A - 2 + 1/A) \\ G. C. Greubel, Jun 22 2018

Crossrefs

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

Sequence in context: A233739 A279036 A182699 * A180964 A237668 A366754

Adjacent sequences: A058593 A058594 A058595 * A058597 A058598 A058599

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved