login
McKay-Thompson series of class 10a for Monster.
1

%I #25 May 22 2018 22:21:59

%S 1,8,35,100,260,548,1191,2340,4525,8320,14838,25828,44070,73500,

%T 120695,194408,309459,485400,753025,1154260,1751419,2631924,3920625,

%U 5790400,8486720,12343172,17832027,25588580,36495125,51738640

%N McKay-Thompson series of class 10a for Monster.

%C The convolution square of this sequence is A007251 except for the constant term: T10a(q)^2 = T5A(q^2) + 16. - _G. A. Edgar_, Apr 03 2017

%H G. C. Greubel, <a href="/A058102/b058102.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..500 from G. A. Edgar)

%H D. Alexander, C. Cummins, J. McKay and C. Simons, <a href="http://oeis.org/A007242/a007242_1.pdf">Completely Replicable Functions</a>, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.

%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 a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4)*5^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017

%e T10a = 1/q + 8*q + 35*q^3 + 100*q^5 + 260*q^7 + 548*q^9 + 1191*q^11 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 100; T5A := 6 +(eta[q]/eta[q^5] )^6 + 125*(eta[q^5]/eta[q])^6; a:= CoefficientList[Series[((q (T5A + 16) + O[q]^nmax // Normal /. {q -> q^2}) + O[q]^nmax)^(1/2) // Normal, {q, 0, nmax}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, May 05 2018 *)

%o (PARI)

%o t(q)=(eta(q)/eta(q^5))^6 / q + 6 + 125 * q * (eta(q^5)/eta(q))^6; \\ A007251

%o s(q)=sqrt(t(q^2) + 16);

%o v=Vec( s('q+O('q^100) ) );

%o vector(#v\2,n,v[2*n-1])

%o \\ _Joerg Arndt_, May 19 2018

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

%K nonn

%O 0,2

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