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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

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

Index entries for McKay-Thompson series for Monster simple group

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

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A222882 A236335 A016724 * A321285 A091434 A027633

Adjacent sequences:  A058654 A058655 A058656 * A058658 A058659 A058660

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 January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)