A058776 McKay-Thompson series of class 119A for Monster.

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 10, 10, 11, 12, 13, 13, 15, 16, 18, 18, 21, 21, 23, 24, 27, 28, 31, 33, 35, 37, 40, 42, 46, 48, 53, 55, 59, 62, 68, 71, 76, 81, 86, 90, 97, 102, 110, 115, 124, 129

Offset

-1,13

Links

Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..2500 from G. C. Greubel)

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 + A*B/q in powers of q, where A = G(q^119)*G(q) + q^24*H(q^119)*H(q), B = G(q^17)*H(q^7) - q^2*H(q^17)*G(q^7), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jul 01 2018

a(n) ~ exp(4*Pi*sqrt(n/119)) / (sqrt(2) * 119^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T119A = 1/q + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 + ...

Mathematica

QP := QPochhammer; 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^119]*G[x] + x^24*H[x^119]*H[x]; B:= G[x^17]*H[x^7] - x^2*H[x^17]*G[x^7]; a:= CoefficientList[Series[-x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

Crossrefs

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

Sequence in context: A294107 A240874 A029379 * A233296 A029228 A029215

Adjacent sequences: A058773 A058774 A058775 * A058777 A058778 A058779

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 19 2014

Status

approved