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A058657 McKay-Thompson series of class 38A for Monster. 2
1, 0, 2, 2, 5, 4, 9, 8, 16, 16, 25, 26, 44, 44, 67, 70, 103, 108, 155, 166, 230, 248, 333, 362, 482, 524, 680, 748, 959, 1052, 1330, 1468, 1834, 2028, 2500, 2770, 3394, 3760, 4561, 5066, 6100, 6772, 8102, 9000, 10702, 11888, 14048, 15612, 18360, 20396, 23865 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of -1/2 + (17/4 + T19A(q) + T19A(q^2) )^(1/2), where T19A(q) = A058549, in powers of q. - G. C. Greubel, Jun 24 2018
a(n) ~ exp(2*Pi*sqrt(2*n/19)) / (2^(3/4) * 19^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018
EXAMPLE
T38A = 1/q + 2*q + 2*q^2 + 5*q^3 + 4*q^4 + 9*q^5 + 8*q^6 + 16*q^7 + 16*q^8 + ...
MATHEMATICA
QP := QPochhammer; eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; G[q_] := 1/(QP[q, q^5]*QP[q^4, q^5]); H[q_] := 1/(QP[q^2, q^5]*QP[q^3, q^5]); T19A := -3 + (G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q; a:= CoefficientList[Series[q*(-1/2 + (17/4 + T19A + (T19A /. {q -> q^2}) + O[q]^nmax)^(1/2)), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)
CROSSREFS
Sequence in context: A222882 A236335 A016724 * A321285 A091434 A027633
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 20 2014
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)