A058638 McKay-Thompson series of class 34A for Monster.

1, 0, 3, 2, 5, 6, 12, 12, 22, 22, 39, 40, 63, 68, 106, 112, 164, 182, 257, 282, 390, 432, 584, 652, 859, 964, 1253, 1404, 1794, 2024, 2556, 2880, 3594, 4054, 5016, 5662, 6930, 7830, 9516, 10744, 12959, 14640, 17546, 19800, 23590, 26612, 31536, 35560, 41919

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 -1/2 + ( 25/4 + T17A(q) + T17A(q^2) )^(1/2), where T17A(q) = A058530, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(2*n/17)) / (2^(3/4) * 17^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T34A = 1/q + 3*q + 2*q^2 + 5*q^3 + 6*q^4 + 12*q^5 + 12*q^6 + 22*q^7 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q];  nmax = 110;  A:= q^(1/2)*(eta[q^4]^2 *(eta[q^34]^5/(eta[q]*eta[q^2]*eta[q^17]^3*eta[q^68]^2)) - eta[q^2]^5*(eta[q^68]^2/(eta[q]^3*eta[q^4]^2*eta[q^17]*eta[q^34]))); T17A := (A^2 - 2*q)/q; T34A := -q/2 + q*((25/4) + T17A + (T17A /. {q -> q^2}) + O[q]^nmax)^(1/2);  a:= CoefficientList[Series[T34A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

Crossrefs

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

Sequence in context: A338209 A240574 A050061 * A201218 A139140 A047074

Adjacent sequences: A058635 A058636 A058637 * A058639 A058640 A058641

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved