A007256 - OEIS

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A007256

McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
(Formerly M4962)

1, 0, 15, -32, 87, -192, 343, -672, 1290, -2176, 3705, -6336, 10214, -16320, 25905, -39936, 61227, -92928, 138160, -204576, 300756, -435328, 626727, -897408, 1271205, -1790592, 2508783, -3487424, 4824825, -6641664, 9083400, -12371904, 16778784, -22630912, 30407112, -40703040, 54238342, -72018624

(list; graph; refs; listen; history; text; internal format)

OFFSET

-1,3

COMMENTS

Apart from a(0) same as A045486 and A121666. [Joerg Arndt, Apr 09 2016]

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

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

EXAMPLE

T6C = 1/q + 15*q - 32*q^2 + 87*q^3 - 192*q^4 + 343*q^5 - 672*q^6 + ...

MATHEMATICA

QP = QPochhammer; A007256[n_] := SeriesCoefficient[((QP[q]*(QP[q^3]) /(QP[q^2]*QP[q^6])))^6/q^1 + 6, {q, 0, n}]; Join[{1}, Table[A007256[n], {n, 0, 50}]] (* G. C. Greubel, Oct 09 2017 *)

PROG

(PARI) N=66; q='q+O('q^N); Vec( ((eta(q^1)*eta(q^3))/ (eta(q^2)*eta(q^6)))^6/q + 6 ) \\ Joerg Arndt, Apr 09 2016

CROSSREFS

Cf. A045486.

Sequence in context: A098848 A055809 A112147 * A199743 A331551 A180815

Adjacent sequences: A007253 A007254 A007255 * A007257 A007258 A007259

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved