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A058740 McKay-Thompson series of class 66B for Monster. 1
1, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 6, 7, 8, 9, 10, 12, 14, 17, 19, 21, 24, 29, 33, 38, 43, 48, 54, 61, 70, 79, 88, 98, 111, 124, 140, 157, 174, 193, 214, 239, 266, 295, 326, 361, 398, 441, 488, 538, 592, 650, 715, 786, 864, 948, 1041, 1138, 1246, 1364, 1492 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,6

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 + A, where A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( eta(q)*eta(q^6)*eta(q^11)*eta(q^66)), in powers of q. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(2*Pi*sqrt(2*n/33)) / (2^(3/4) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T66B = 1/q + q + q^2 + q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 3*q^7 + 3*q^8 + 4*q^9 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^3]*eta[q^22]* eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]);  a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( q*eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); Vec(-1 + A) \\ G. C. Greubel, Jun 29 2018

CROSSREFS

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

Sequence in context: A173910 A036846 A227396 * A160642 A110868 A110869

Adjacent sequences:  A058737 A058738 A058739 * A058741 A058742 A058743

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified January 17 16:53 EST 2019. Contains 319235 sequences. (Running on oeis4.)