A058598 McKay-Thompson series of class 26a for Monster.

1, 2, 4, 6, 13, 16, 27, 38, 57, 78, 112, 146, 205, 272, 367, 476, 634, 816, 1059, 1354, 1738, 2196, 2791, 3492, 4387, 5460, 6798, 8396, 10383, 12740, 15645, 19084, 23288, 28262, 34297, 41412, 49985, 60088, 72184, 86404, 103354, 123214, 146779, 174354, 206895, 244900, 289606, 341660, 402685

Offset

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of (6 + f)^(1/2), where f = A034318, 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 + 2*q + 4*q^3 + 6*q^5 + 13*q^7 + 16*q^9 + 27*q^11 + 38*q^13 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax := 130; A:= (eta[q]/eta[q^13])^2;
f := A + 13/A; a:= CoefficientList[Series[(q*(6 + f) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)

Crossrefs

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

Sequence in context: A307617 A325278 A110980 * A332241 A319110 A278031

Adjacent sequences: A058595 A058596 A058597 * A058599 A058600 A058601

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 22 2018

Status

approved