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A045484 McKay-Thompson series of class 6A for Monster. 4
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: A197101 A245674 A166052 * A113152 A265585 A060051

Adjacent sequences:  A045481 A045482 A045483 * A045485 A045486 A045487

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)