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A112162 McKay-Thompson series of class 24b for the Monster group. 1
1, 1, 7, 9, 10, 23, 38, 47, 75, 112, 148, 217, 293, 385, 553, 728, 928, 1272, 1670, 2111, 2765, 3566, 4504, 5784, 7300, 9123, 11592, 14458, 17838, 22342, 27668, 33884, 41843, 51344, 62548, 76515, 92989, 112514, 136687, 164961, 198190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2500

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^4)/(eta(q)* eta(q^12)))^2, in powers of q. - G. C. Greubel, Jun 25 2018

a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T24b = 1/q + q + 7*q^3 + 9*q^5 + 10*q^7 + 23*q^9 + 38*q^11 + 47*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^3]*eta[q^4]/(eta[q]*eta[q^12]))^2; a := CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^4)/(eta(q)*eta(q^12)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 25 2018

CROSSREFS

Sequence in context: A095034 A118621 A117933 * A058483 A176326 A283056

Adjacent sequences:  A112159 A112160 A112161 * A112163 A112164 A112165

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)