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A058563 McKay-Thompson series of class 21A for Monster. 3
1, 0, 6, 6, 15, 30, 41, 66, 111, 146, 222, 336, 463, 642, 942, 1238, 1698, 2334, 3090, 4098, 5514, 7136, 9336, 12216, 15673, 20142, 26013, 32880, 41820, 53070, 66609, 83568, 105039, 130482, 162321, 201708, 248802, 306642, 377955, 462596, 566223, 692064 (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

a(n) ~ exp(4*Pi*sqrt(n/21)) / (sqrt(2) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018

Expansion of A + 1 + 7/A, where A = eta(q)*eta(q^3)/(eta(q^7)*eta(q^21)), in powers of q. - G. C. Greubel, Jun 18 2018

EXAMPLE

T21A = 1/q + 6*q + 6*q^2 + 15*q^3 + 30*q^4 + 41*q^5 + 66*q^6 + 111*q^7 + ...

MATHEMATICA

CoefficientList[Series[((QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]))^2, {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= eta[q]*eta[q^3]/(eta[q^7] *eta[q^21]); a:= CoefficientList[Series[1 + A + 7/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)*eta(q^3)/(q*eta(q^7)*eta(q^21)); Vec(A + 1 + 7/A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

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

Sequence in context: A256675 A290931 A257372 * A175561 A315810 A315811

Adjacent sequences:  A058560 A058561 A058562 * A058564 A058565 A058566

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 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)