A058536 - OEIS

A058536

McKay-Thompson series of class 18a for Monster.

1, 0, 1, 4, 0, -4, 10, 0, 6, 20, 0, -4, 35, 0, 1, 60, 0, -4, 100, 0, 16, 164, 0, -28, 261, 0, 32, 400, 0, -28, 600, 0, 22, 884, 0, -32, 1291, 0, 68, 1864, 0, -116, 2656, 0, 140, 3740, 0, -120, 5205, 0, 100, 7184, 0, -144, 9842, 0, 262, 13388, 0, -392, 18082, 0, 449, 24244, 0, -420, 32300

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OFFSET

-1,4

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..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^2/A, where q*(eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18) ))^4, in powers of q. - G. C. Greubel, Jun 20 2018

EXAMPLE

T18a = 1/q + q + 4*q^2 - 4*q^4 + 10*q^5 + 6*q^7 + 20*q^8 - 4*q^10 + 35*q^11 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q*(eta[q^6]*eta[q^9]/(eta[q^3]* eta[q^18]))^4; a:= CoefficientList[Series[A + q^2/A, {q, 0, 80}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^4; Vec(A + q^2/A) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

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

Sequence in context: A101980 A209134 A281297 * A371377 A154854 A151672

Adjacent sequences: A058533 A058534 A058535 * A058537 A058538 A058539

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(24) onward added by G. C. Greubel, Jun 20 2018

STATUS

approved