A058594 - OEIS

%I #18 Jun 28 2018 04:07:01

%S 1,0,4,5,10,16,25,36,55,75,110,150,209,280,385,504,675,880,1155,1485,

%T 1925,2450,3136,3960,5010,6276,7875,9784,12175,15040,18576,22800,

%U 27986,34155,41670,50604,61400,74204,89605,107800,129568,155250,185810,221760,264385

%N McKay-Thompson series of class 25A for Monster.

%H G. C. Greubel, <a href="/A058594/b058594.txt">Table of n, a(n) for n = -1..1000</a>

%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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1602206&amp;messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum

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

%F Expansion of A + 1 + 5/A, where A = eta(q)/eta(q^25), in powers of q. - _G. C. Greubel_, Jun 22 2018

%F a(n) ~ exp(4*Pi*sqrt(n)/5) / (sqrt(10) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T25A = 1/q + 4*q + 5*q^2 + 10*q^3 + 16*q^4 + 25*q^5 + 36*q^6 + 55*q^7 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q];  A:= (eta[q]/eta[q^25]); a:= CoefficientList[Series[1 + A + 5/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 22 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q)/(q*eta(q^25)); Vec(A + 1 + 5/A) \\ _G. C. Greubel_, Jun 22 2018

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

%K nonn

%O -1,3

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

%E More terms from _Michel Marcus_, Feb 20 2014