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A007254 McKay-Thompson series of class 6A for Monster.
(Formerly M5355)
5
1, 0, 79, 352, 1431, 4160, 13015, 31968, 81162, 183680, 412857, 864320, 1805030, 3564864, 7000753, 13243392, 24805035, 45168896, 81544240, 143832672, 251550676, 432030080, 735553575, 1233715328, 2052941733 (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

Vaclav Kotesovec, 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.

Wikipedia, Generalized Monstrous Moonshine

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) = A121665(n) + A226235(n) = A121666(n) + 64*A123653(n) = A121667(n) + 81*A284607(n) for n > 0. - Seiichi Manyama, Mar 30 2017

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 30 2017

EXAMPLE

T6A = 1/q + 79*q + 352*q^2 + 1431*q^3 + 4160*q^4 + 13015*q^5 + 31968*q^6 + ...

MATHEMATICA

nmax = 50; Flatten[{1, 0, Rest[Rest[CoefficientList[Series[Product[((1 + x^k)/(1 + x^(3*k)))^12, {k, 1, nmax}] + x^2*Product[((1 + x^(3*k))/(1 + x^k))^12, {k, 1, nmax}], {x, 0, nmax}], x]]]}] (* Vaclav Kotesovec, Mar 30 2017 *)

CROSSREFS

Cf. A045484.

Sequence in context: A157507 A142897 A142330 * A142439 A200847 A132252

Adjacent sequences:  A007251 A007252 A007253 * A007255 A007256 A007257

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 17 01:56 EDT 2017. Contains 290631 sequences.