A034322 McKay-Thompson series of class 71A for Monster.

1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 7, 8, 10, 11, 13, 14, 17, 19, 22, 24, 29, 31, 36, 40, 46, 50, 58, 63, 72, 79, 89, 98, 111, 121, 136, 149, 167, 182, 204, 222, 247, 270, 299, 326, 362, 393, 434, 473, 521, 566, 623, 676, 742, 806, 882, 956, 1047, 1133

Offset

-1,7

Comments

Also McKay-Thompson series of class 71B for Monster. - Michel Marcus, Feb 19 2014

Links

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

I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

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

a(n) ~ exp(4*Pi*sqrt(n/71)) / (sqrt(2) * 71^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 05 2018

Example

T71A = 1/q + q + q^2 + q^3 + q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 3*q^8 + 4*q^9 + ...

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:= CoefficientList[Series[G[x^71]*H[x] - x^14*H[x^71]*G[x], {x, 0, 80}], x]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jul 05 2018 *)

Crossrefs

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

Sequence in context: A181972 A356737 A058747 * A362612 A319169 A050365

Adjacent sequences: A034319 A034320 A034321 * A034323 A034324 A034325

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved