A007262 McKay-Thompson series of class 6c for Monster. (Formerly M4078)

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

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