A058594 McKay-Thompson series of class 25A for Monster.

1, 0, 4, 5, 10, 16, 25, 36, 55, 75, 110, 150, 209, 280, 385, 504, 675, 880, 1155, 1485, 1925, 2450, 3136, 3960, 5010, 6276, 7875, 9784, 12175, 15040, 18576, 22800, 27986, 34155, 41670, 50604, 61400, 74204, 89605, 107800, 129568, 155250, 185810, 221760, 264385

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 + 1 + 5/A, where A = eta(q)/eta(q^25), in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(4*Pi*sqrt(n)/5) / (sqrt(10) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T25A = 1/q + 4*q + 5*q^2 + 10*q^3 + 16*q^4 + 25*q^5 + 36*q^6 + 55*q^7 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q];  A:= (eta[q]/eta[q^25]); a:= CoefficientList[Series[1 + A + 5/A, {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)/(q*eta(q^25)); Vec(A + 1 + 5/A) \\ G. C. Greubel, Jun 22 2018

Crossrefs

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

Sequence in context: A118735 A002970 A073611 * A285289 A022309 A049897

Adjacent sequences: A058591 A058592 A058593 * A058595 A058596 A058597

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved