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A007257 McKay-Thompson series of class 6D for Monster.
(Formerly M2147)
3
1, 0, -2, 28, -27, -52, 136, -108, -162, 620, -486, -760, 1970, -1404, -1940, 6048, -4293, -6100, 15796, -10692, -14264, 40232, -27108, -36496, 93285, -61020, -79054, 211624, -137781, -179296, 451680, -288360, -365780 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
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 H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
Expansion of 4 + (eta(q)*eta(q^2)/(eta(q^3)*eta(q^6)))^4 in powers of q. - G. C. Greubel, Jan 30 2018
EXAMPLE
T6D = 1/q - 2*q + 28*q^2 - 27*q^3 - 52*q^4 + 136*q^5 - 108*q^6 - 162*q^7 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[4 + (eta[q] *eta[q^2]/(eta[q^3]*eta[q^6]))^4, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 30 2018 *)
PROG
(PARI) q='q+O('q^30); a= 4 + (eta(q)*eta(q^2)/(eta(q^3)*eta(q^6)))^4/q; Vec(a) \\ G. C. Greubel, Jun 02 2018
CROSSREFS
Cf. A045487.
Sequence in context: A362288 A056013 A363403 * A045487 A022376 A177829
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)