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A007258 McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
(Formerly M4052)
8
1, 0, 6, 4, -3, -12, -8, 12, 30, 20, -30, -72, -46, 60, 156, 96, -117, -300, -188, 228, 552, 344, -420, -1008, -603, 732, 1770, 1048, -1245, -2976, -1776, 2088, 4908, 2900, -3420, -7992, -4658, 5460, 12756, 7408, -8583, -19944, -11564, 13344, 30756, 17744, -20448, -46944, -26916 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
COMMENTS
Also normalized Hauptmodul for Gamma_0(6).
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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).
J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.
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.
Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]
Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.
FORMULA
Expansion of 5 + eta(q)^5*eta(q^3)/(eta(q^2)*eta(q^6)^5) in powers of q.
EXAMPLE
T6E = 1/q + 6*q + 4*q^2 - 3*q^3 - 12*q^4 - 8*q^5 + 12*q^6 + 30*q^7 + ...
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Essentially same as A045488.
Sequence in context: A020794 A268818 A112148 * A045488 A082530 A099404
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)