|
%I #28 Jun 07 2018 02:51:45
%S 1,0,-2,1,0,2,1,0,0,-1,0,-4,-1,0,4,0,0,2,1,0,-8,2,0,8,0,0,2,-2,0,-16,
%T -3,0,16,-1,0,4,4,0,-28,4,0,28,1,0,8,-4,0,-48,-6,0,46,-1,0,12,5,0,-80,
%U 8,0,76,1,0,20,-8,0,-126,-10,0,120,-2,0,32,11,0,-196,14,0,184,4,0,48
%N McKay-Thompson series of class 18A for the Monster group.
%H G. C. Greubel, <a href="/A058531/b058531.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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F a(3*n) = 0, a(3*n - 1) = A062242(n), a(3*n + 1) = -2*A092848(n). - _Michael Somos_, Mar 17 2004
%F Expansion of F - 2/F, where F = q^(1/3) * eta(q^2) * eta(q^3)^3 / (eta(q) * eta(q^6)^3), in powers of q. - _G. C. Greubel_, May 28 2018
%e T18A = 1/q - 2*q + q^2 + 2*q^4 + q^5 - q^8 - 4*q^10 - q^11 + 4*q^13 + 2*q^16 + ...
%t a[ n_] := SeriesCoefficient[ 1 + 1/q QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^9] QPochhammer[ q^18]), {q, 0, n}]; (* _Michael Somos_, Apr 26 2015 *)
%o (PARI) {a(n) = my(A); if( n<1, n==-1, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A) / (eta(x^9 + A) * eta(x^18 + A)), n))}; /* _Michael Somos_, Mar 17 2004 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A062242, A092848.
%K sign
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
|
