A045480 McKay-Thompson series of class 3A for Monster. Expansion of Hauptmodul for X_0^{+}(3).

1, 6, 783, 8672, 65367, 371520, 1741655, 7161696, 26567946, 90521472, 288078201, 864924480, 2469235686, 6748494912, 17746495281, 45086909440, 111066966315, 266057139456, 621284327856, 1417338712800, 3164665156308

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..1002

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

N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ exp(4*Pi*sqrt(n/3)) / (sqrt(2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 01 2017

Mathematica

QP = QPochhammer; A = q*O[q]^20; A = (QP[q^3 + A]/QP[q + A])^12; s = (1 + 27*q*A)^2/A - 36*q; CoefficientList[s, q] (* Jean-François Alcover, Mar 08 2017, after Michael Somos (A007243) *)

Crossrefs

Apart from constant term, same as A007243, A030197.

Sequence in context: A242850 A364273 A020542 * A006114 A341554 A365511

Adjacent sequences: A045477 A045478 A045479 * A045481 A045482 A045483

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved