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A007256 McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
(Formerly M4962)
3
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
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.
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
KEYWORD
sign
AUTHOR
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)