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A058739 McKay-Thompson series of class 66A for Monster. 2
1, 0, 2, 0, 1, 2, 2, 2, 4, 2, 5, 6, 7, 6, 12, 8, 13, 14, 19, 16, 25, 20, 31, 32, 40, 38, 55, 48, 64, 68, 83, 80, 108, 102, 130, 136, 163, 162, 209, 200, 247, 260, 306, 308, 383, 378, 455, 478, 553, 566, 683, 686, 805, 848, 972, 1004, 1183, 1204, 1395, 1468 (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^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

T66A = 1/q + 2*q + q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 4*q^7 + 2*q^8 + 5*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 + 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(A - 1 + 1/A) \\ G. C. Greubel, Jun 29 2018

CROSSREFS

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

Sequence in context: A254212 A033773 A029275 * A128627 A105422 A166291

Adjacent sequences:  A058736 A058737 A058738 * A058740 A058741 A058742

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 06:41 EST 2019. Contains 319207 sequences. (Running on oeis4.)