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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
OFFSET
-1,3
LINKS
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 20 2014
STATUS
approved