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A112168 McKay-Thompson series of class 27e for the Monster group. 1
1, -1, 2, 3, 0, 1, 3, -2, 3, 7, -4, 5, 11, -3, 7, 14, -5, 9, 23, -11, 19, 35, -11, 20, 44, -19, 31, 66, -27, 45, 91, -32, 57, 118, -45, 75, 164, -68, 112, 222, -77, 134, 279, -109, 181, 376, -148, 242, 490, -178, 304, 617, -233, 385, 803, -314, 517, 1032, -372, 626, 1281, -487, 803 (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 (T9b - 3*q)^(1/3), where T9b = A114146, in powers of q. - G. C. Greubel, Jun 25 2018

EXAMPLE

T27e = 1/q - q^2 + 2*q^5 + 3*q^8 + q^14 + 3*q^17 - 2*q^20 + 3*q^23 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q*(eta[q^3]/eta[q^9] )^4; T9b := A + 9*q^2/A; a:= CoefficientList[Series[(T9b - 3*q + O[q]^nmax)^(1/3), {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^9))^4; T9b = A + 9*q^2/A; Vec((T9b - 3*q)^(1/3)) \\ G. C. Greubel, Jun 25 2018

CROSSREFS

Sequence in context: A106730 A089652 A195467 * A072516 A320782 A191588

Adjacent sequences:  A112165 A112166 A112167 * A112169 A112170 A112171

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 20 23:17 EST 2019. Contains 319336 sequences. (Running on oeis4.)