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A058671 McKay-Thompson series of class 42A for Monster. 1
1, 0, 2, 2, 3, 2, 9, 6, 11, 14, 18, 16, 31, 30, 46, 50, 66, 66, 106, 102, 146, 160, 204, 216, 297, 306, 401, 448, 552, 594, 777, 816, 1023, 1134, 1377, 1492, 1858, 1998, 2427, 2684, 3183, 3488, 4219, 4566, 5429, 6000, 7020, 7688, 9115, 9918, 11593, 12806 (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 A + 2 + 1/A, where A = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21) )/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T42A = 1/q + 2*q + 2*q^2 + 3*q^3 + 2*q^4 + 9*q^5 + 6*q^6 + 11*q^7 + 14*q^8 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A := ((eta[q]*eta[q^6]*eta[q^14]* eta[q^21])/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42]))^2; a := CoefficientList[Series[2 + A + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

PROG

(PARI) q='q+O('q^50); A = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21))/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2/q; Vec(A + 2 + 1/A) \\ G. C. Greubel, Jun 24 2018

CROSSREFS

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

Sequence in context: A016012 A069138 A179592 * A016002 A098189 A162733

Adjacent sequences:  A058668 A058669 A058670 * A058672 A058673 A058674

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 October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)