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A034322 McKay-Thompson series of class 71A for Monster. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A056039 A181972 A058747 * A319169 A050365 A029026

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

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)