A058742 McKay-Thompson series of class 68A for Monster.

1, 1, 1, 0, 2, 1, 3, 2, 4, 3, 6, 4, 7, 7, 10, 8, 14, 12, 18, 16, 23, 22, 30, 28, 39, 37, 49, 46, 62, 60, 78, 76, 97, 96, 122, 120, 150, 150, 185, 184, 228, 229, 278, 280, 338, 342, 410, 416, 495, 506, 597, 610, 718, 736, 859, 884, 1026, 1058, 1224, 1262, 1453, 1505, 1722, 1784, 2039

Offset

-1,5

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 sqrt(T34A + 2), where T34A = A058638, in powers of q. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(2*Pi*sqrt(n/17)) / (2 * 17^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T68A = 1/q + q + q^3 + 2*q^7 + q^9 + 3*q^11 + 2*q^13 + 4*q^15 + 3*q^17 + ...

Mathematica

QP := QPochhammer; nmax = 260; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]* QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2];  A := G[x^34]*G[x] + x^7*H[x^34]*H[x]; B:= G[x^17]*H[x^2] - x^3*H[x^17]*G[x^2]; T34A := -2 + (A*B)^2/x; a:= CoefficientList[Series[(x*(2 + T34A) + O[x]^nmax)^(1/2), {x, 0, 100}], x]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 29 2018 *)

Crossrefs

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

Sequence in context: A265253 A161227 A115584 * A029140 A008584 A352833

Adjacent sequences: A058739 A058740 A058741 * A058743 A058744 A058745

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 29 2018

Status

approved