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A058571
McKay-Thompson series of class 24A for Monster.
2
1, 3, 3, 7, 18, 21, 30, 57, 75, 104, 156, 207, 293, 411, 525, 712, 984, 1248, 1622, 2169, 2757, 3530, 4560, 5736, 7284, 9249, 11472, 14374, 18078, 22242, 27484, 34140, 41787, 51184, 62796, 76317, 92893, 112998, 136275, 164671
OFFSET
0,2
COMMENTS
Convolution cube of A112206. - Vaclav Kotesovec, Mar 12 2017
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 (terms 0..50 from G. A. Edgar)
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of q^(1/2) * (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) in powers of q. - G. A. Edgar, Mar 11 2017
a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 12 2017
EXAMPLE
T24A = 1/q + 3*q + 3*q^3 + 7*q^5 + 18*q^7 + 21*q^9 + 30*q^11 + 57*q^13 + ...
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 12 2017 *)
PROG
(PARI) q='q+O('q^66); Vec( (eta(q^2)^6 * eta(q^6)^6 / (eta(q)^3 * eta(q^3)^3 * eta(q^4)^3 * eta(q^12)^3)) ) \\ Joerg Arndt, Mar 11 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Offset corrected by N. J. A. Sloane, Feb 17 2014
More terms from G. A. Edgar, Mar 11 2017
STATUS
approved