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A058676 McKay-Thompson series of class 42b for Monster. 1
1, 2, 1, 1, 5, 4, 7, 10, 12, 12, 22, 22, 29, 41, 46, 55, 73, 81, 102, 127, 149, 175, 223, 246, 299, 365, 417, 488, 594, 671, 785, 934, 1069, 1232, 1465, 1653, 1918, 2230, 2536, 2903, 3379, 3814, 4372, 5031, 5679, 6456, 7423, 8336, 9477, 10798, 12150, 13701, 15595, 17463, 19696, 22273 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + q/A, where A = q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))), in powers of q. - G. C. Greubel, Jun 26 2018

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T42b = 1/q + 2*q + q^3 + q^5 + 5*q^7 + 4*q^9 + 7*q^11 + 10*q^13 + 12*q^15 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^3]*eta[q^7]/( eta[q]*eta[q^21])); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))); Vec(A+q/A) \\ G. C. Greubel, Jun 26 2018

CROSSREFS

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

Sequence in context: A050145 A222573 A222679 * A147649 A147644 A158188

Adjacent sequences:  A058673 A058674 A058675 * A058677 A058678 A058679

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 26 2018

STATUS

approved

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Last modified January 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)