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A058596 McKay-Thompson series of class 26A for Monster. 1
1, 0, 4, 4, 10, 12, 26, 28, 51, 60, 102, 116, 189, 220, 336, 396, 575, 684, 974, 1152, 1588, 1892, 2554, 3032, 4017, 4780, 6234, 7404, 9519, 11292, 14368, 17012, 21402, 25308, 31552, 37228, 46039, 54216, 66566, 78232, 95384, 111892, 135624, 158764, 191359 (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^2)*eta(q^13)/(eta(q)* eta(q^26)))^2, in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(2*Pi*sqrt(2*n/13)) / (2^(3/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T26A = 1/q + 4*q + 4*q^2 + 10*q^3 + 12*q^4 + 26*q^5 + 28*q^6 + 51*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^13]/(eta[q]* eta[q^26]))^2; a:= CoefficientList[Series[-2 + e26B + 1/e26B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^13)/(eta(q)*eta(q^26)))^2/q; Vec(A - 2 + 1/A) \\ G. C. Greubel, Jun 22 2018

CROSSREFS

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

Sequence in context: A233739 A279036 A182699 * A180964 A237668 A209423

Adjacent sequences:  A058593 A058594 A058595 * A058597 A058598 A058599

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 14 15:12 EDT 2019. Contains 328019 sequences. (Running on oeis4.)