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McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
(Formerly M4052)
8

%I M4052 #27 May 09 2018 22:58:22

%S 1,0,6,4,-3,-12,-8,12,30,20,-30,-72,-46,60,156,96,-117,-300,-188,228,

%T 552,344,-420,-1008,-603,732,1770,1048,-1245,-2976,-1776,2088,4908,

%U 2900,-3420,-7992,-4658,5460,12756,7408,-8583,-19944,-11564,13344,30756,17744,-20448,-46944,-26916

%N McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).

%C Also normalized Hauptmodul for Gamma_0(6).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A007258/b007258.txt">Table of n, a(n) for n = -1..1000</a>

%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H J. McKay and A. Sebbar, <a href="http://dx.doi.org/10.1007/s002080000116">Fuchsian groups, automorphic functions and Schwarzians</a>, Math. Ann., 318 (2000), 255-275.

%H J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.

%H Morris Newman, <a href="/A002507/a002507.pdf">Construction and application of a class of modular functions, II</a>, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

%H Morris Newman, <a href="http://plms.oxfordjournals.org/content/s3-9/3/373.extract">Construction and application of a class of modular functions (II)</a>. Proc. London Math. Soc. (3) 9 1959 373-387.

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of 5 + eta(q)^5*eta(q^3)/(eta(q^2)*eta(q^6)^5) in powers of q.

%e T6E = 1/q + 6*q + 4*q^2 - 3*q^3 - 12*q^4 - 8*q^5 + 12*q^6 + 30*q^7 + ...

%t QP = QPochhammer; s = 5*q + QP[q]^5*(QP[q^3]/(QP[q^2]*QP[q^6]^5)) + O[q]^50; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 15 2015 *)

%o (PARI) q='q+O('q^30); Vec(5 +(eta(q)^5*eta(q^3))/(q*eta(q^2)*eta(q^6)^5)) \\ _G. C. Greubel_, May 09 2018

%Y Essentially same as A045488.

%K sign

%O -1,3

%A _N. J. A. Sloane_