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A058659 McKay-Thompson series of class 39A for Monster. 2
1, 0, 3, 1, 3, 6, 6, 9, 15, 15, 21, 30, 34, 42, 60, 66, 84, 108, 127, 153, 201, 226, 276, 342, 400, 471, 585, 667, 795, 954, 1103, 1290, 1551, 1771, 2073, 2442, 2807, 3246, 3816, 4346, 5028, 5838, 6662, 7638, 8856, 10040, 11505, 13212, 14991, 17064, 19560 (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 - 1 + 1/A, where A = (eta(q^3)*eta(q^13)/(eta(q)* eta(q^39))), in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T39A = 1/q + 3*q + q^2 + 3*q^3 + 6*q^4 + 6*q^5 + 9*q^6 + 15*q^7 + 15*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^13]/( eta[q]* eta[q^39])); a := CoefficientList[Series[A  - 1 + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q^3)*eta(q^13)/(q*eta(q)*eta(q^39)); Vec(A - 1 +1/A) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A137338 A176106 A302867 * A053642 A171961 A205121

Adjacent sequences:  A058656 A058657 A058658 * A058660 A058661 A058662

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 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)