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A007262 McKay-Thompson series of class 6c for Monster.
(Formerly M4078)
6
1, -6, 9, 16, -66, 54, 98, -300, 243, 364, -1128, 828, 1221, -3498, 2511, 3528, -9876, 6804, 9358, -25428, 17217, 23068, -61644, 40824, 53916, -141318, 92340, 119912, -310554, 199980, 256792, -656436, 418311, 530960, -1344144, 847584, 1066157, -2673372, 1671741, 2084464, -5186118, 3216834, 3981926, -9832752, 6057504, 7445924, -18269124, 11181636, 13661725, -33315852, 20274948, 24630344, -59740716 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

G.f.: (E(q^2)/E(q^6))^6 / q where E(q) = Product_{n>=1} (1 - q^n); note that every second term is zero and is omitted in this sequence, cf. the Pari/GP code. - Joerg Arndt, Apr 09 2016

EXAMPLE

T6c = 1/q - 6*q + 9*q^3 + 16*q^5 - 66*q^7 + 54*q^9 + 98*q^11 - 300*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QP0chhammer[q]; a[n_]:= SeriesCoefficient[ q^(-1)*(eta[q^2]/ eta[q^6])^6, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 25 2018 *)

PROG

(PARI) N=66; q='q+O('q^N); Vec( (eta(q^1)/eta(q^3))^6/q ) \\ Joerg Arndt, Apr 09 2016

CROSSREFS

Cf. A132107.

Sequence in context: A031326 A290791 A132107 * A129317 A316067 A316068

Adjacent sequences:  A007259 A007260 A007261 * A007263 A007264 A007265

KEYWORD

sign

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Joerg Arndt, Apr 09 2016

STATUS

approved

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Last modified October 15 13:38 EDT 2019. Contains 328030 sequences. (Running on oeis4.)