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A007263 McKay-Thompson series of class 6d for Monster.
(Formerly M4995)
5
1, 0, 16, -8, 0, 128, 28, 0, 576, -64, 0, 2048, 134, 0, 6304, -288, 0, 17408, 568, 0, 44416, -1024, 0, 106496, 1809, 0, 242480, -3152, 0, 528896, 5316, 0, 1112128, -8704, 0, 2265088, 13990, 0, 4486112 (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

G. C. Greubel, Table of n, a(n) for n = -1..1000 (terms -1..99 from G. A. Edgar)

D. Alexander, C. Cummins, J. McKay, and C. Simons, Completely Replicable Functions, in Groups, Combinatorics & Geometry, (Durham, 1990), pp. 87--98, London Math. Soc. Monograph No. 165.

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

Expansion of (eta(q^3)/eta(q^6))^8 + 16*(eta(q^6)/eta(q^3))^8 in powers of q. - G. A. Edgar, Mar 10 2017

G.f.: T6d = T6F + 16/T6F with T6F as in A007259. - G. A. Edgar, Mar 10 2017

EXAMPLE

T6d = 1/q + 16*q - 8*q^2 + 128*q^4 + 28*q^5 + 576*q^7 - 64*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[(eta[q^3]/ eta[q^6])^8 + 16*(eta[q^6]/eta[q^3])^8, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 25 2018 *)

CROSSREFS

Sequence in context: A070580 A298618 A028579 * A033336 A204325 A102270

Adjacent sequences:  A007260 A007261 A007262 * A007264 A007265 A007266

KEYWORD

sign

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from G. A. Edgar, Mar 03 2017

STATUS

approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)