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A058567 McKay-Thompson series of class 22A for Monster. 1
1, 0, 5, 6, 16, 20, 41, 50, 97, 116, 197, 246, 397, 492, 753, 932, 1378, 1712, 2434, 3028, 4210, 5204, 7075, 8750, 11692, 14396, 18943, 23256, 30220, 36968, 47477, 57890, 73614, 89448, 112726, 136564, 170734, 206136, 255872, 308000, 379801, 455828, 558714 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + 2 + 4/A, where A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22) ))^2, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(3/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T22A = 1/q + 5*q + 6*q^2 + 16*q^3 + 20*q^4 + 41*q^5 + 50*q^6 + 97*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^11]/(eta[q^2]* eta[q^22]))^2;  a:= CoefficientList[Series[q*(2 + A + 4/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A + 2 + 4/A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A104422 A026547 A081283 * A115376 A076650 A068408

Adjacent sequences:  A058564 A058565 A058566 * A058568 A058569 A058570

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 20 2014

STATUS

approved

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Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)