|
%I #24 Jun 21 2018 03:05:56
%S 1,0,5,-2,0,10,-1,0,25,2,0,50,1,0,100,4,0,170,-6,0,305,-2,0,500,2,0,
%T 825,0,0,1300,10,0,2040,-14,0,3100,-5,0,4700,8,0,6950,4,0,10225,20,0,
%U 14800,-28,0,21285,-10,0,30200,14,0,42625,4,0,59500,39,0,82610,-56,0,113690,-20,0
%N Coefficients of replicable function number 15a.
%H G. C. Greubel, <a href="/A058512/b058512.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 Expansion of A + 5*q^2/A, where A = q*(eta(q^3)/eta(q^15))^2, in powers of q. - _G. C. Greubel_, Jun 21 2018
%e T15a = 1/q + 5*q - 2*q^2 + 10*q^4 - q^5 + 25*q^7 + 2*q^8 + 50*q^10 + q^11 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; e15D := q^(1/3)*(eta[q]/eta[q^5])^2;
%t a[n_]:= SeriesCoefficient[(e15D /. {q -> q^3}) + 5*q^2/(e15D /. {q -> q^3}), {q, 0, n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Feb 14 2018 *)
%o (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^3 + A) / eta(x^15 + A))^2; polcoeff( A + 5*x^2 / A, n))}; /* _Michael Somos_, Feb 18 2018 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(24) onward added by _G. C. Greubel_, Feb 14 2018
|
