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A058571 McKay-Thompson series of class 24A for Monster. 2

%I #30 Mar 12 2017 04:26:04

%S 1,3,3,7,18,21,30,57,75,104,156,207,293,411,525,712,984,1248,1622,

%T 2169,2757,3530,4560,5736,7284,9249,11472,14374,18078,22242,27484,

%U 34140,41787,51184,62796,76317,92893,112998,136275,164671

%N McKay-Thompson series of class 24A for Monster.

%C Convolution cube of A112206. - _Vaclav Kotesovec_, Mar 12 2017

%H Vaclav Kotesovec, <a href="/A058571/b058571.txt">Table of n, a(n) for n = 0..2000</a> (terms 0..50 from G. A. Edgar)

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F 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

%F a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Mar 12 2017

%e T24A = 1/q + 3*q + 3*q^3 + 7*q^5 + 18*q^7 + 21*q^9 + 30*q^11 + 57*q^13 + ...

%t 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 *)

%o (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

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, A112206, etc.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Nov 27 2000

%E Offset corrected by _N. J. A. Sloane_, Feb 17 2014

%E More terms from _G. A. Edgar_, Mar 11 2017

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)