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A058648 McKay-Thompson series of class 36a for Monster. 1
1, -1, 0, 2, 2, 0, 3, -1, 0, 4, 0, 0, 5, 0, 0, 8, 2, 0, 11, -4, 0, 16, 4, 0, 21, -4, 0, 26, 2, 0, 34, -1, 0, 44, 4, 0, 58, -9, 0, 74, 12, 0, 93, -9, 0, 116, 4, 0, 143, -5, 0, 178, 12, 0, 221, -20, 0, 272, 24, 0, 332, -20, 0, 402, 14, 0, 487, -13, 0, 588, 24, 0, 710, -42, 0, 854, 50, 0 (list; graph; refs; listen; history; text; internal format)
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/A, where A = q^(1/2)*(eta(q^6)*eta(q^9)/( eta(q^3)* eta(q^18)))^2, in powers of q. - G. C. Greubel, Jun 23 2018

EXAMPLE

T36a = 1/q - q + 2*q^5 + 2*q^7 + 3*q^11 - q^13 + 4*q^17 + 5*q^23 + 8*q^29 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^9]/( eta[q^3]*eta[q^18]))^2; a := CoefficientList[Series[ A -q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A141659 A294519 A123515 * A112174 A089990 A071427

Adjacent sequences:  A058645 A058646 A058647 * A058649 A058650 A058651

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 23 2018

STATUS

approved

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Last modified January 17 06:41 EST 2019. Contains 319207 sequences. (Running on oeis4.)