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A045484

McKay-Thompson series of class 6A for Monster.

1, 2, 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

-1,2

REFERENCES

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.

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; h:= (eta[q]*eta[q^6]/(eta[q^2]* eta[q^3]))^12; g := h - 10 + 1/h; A045484 := CoefficientList[Series[q*g, {q, 0, 60}], q]; Table[A045484[[n]], {n, 1, 50}] (* G. C. Greubel, May 28 2018 *)

PROG

(PARI) q='q+O('q^30); {h =q*(eta(q)*eta(q^6)/(eta(q^2)*eta(q^3)))^12}; Vec(h - 10 + 1/h) \\ G. C. Greubel, May 28 2018

CROSSREFS

Cf. A007254, A121665, A121666, A121667.

Sequence in context: A245674 A342979 A166052 * A113152 A265585 A391924

Adjacent sequences: A045481 A045482 A045483 * A045485 A045486 A045487

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A045484

⇱ A045484 - OEIS