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%I #22 Nov 07 2015 11:23:57
%S 1,-2,-1,2,1,4,-6,-2,2,0,10,-14,-5,8,4,20,-28,-10,14,4,39,-56,-20,28,
%T 10,72,-100,-34,46,16,128,-176,-61,86,30,216,-294,-100,134,44,355,
%U -484,-165,226,79,568,-770,-260,350,116,894,-1208,-408,552,188,1376,-1848,-620,830,276,2087,-2800,-940
%N McKay-Thompson series of class 15D for the Monster group.
%H Vaclav Kotesovec, <a href="/A058511/b058511.txt">Table of n, a(n) for n = 0..1000</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%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 J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of q^(1/3) * (eta(q) / eta(q^5))^2 in powers of q.
%F Euler transform of period 5 sequence [ -2, -2, -2, -2, 0, ...].
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (45 t)) = 5 / f(t) where q = exp(2 Pi i t).
%F G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v^2) * (v - u^2) + 4*u*v.
%F G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = u^2 + u*w + w^2 - v^2 * (u + w) - 5*v.
%e G.f. = 1 - 2*x - x^2 + 2*x^3 + x^4 + 4*x^5 - 6*x^6 - 2*x^7 + 2*x^8 + ...
%e T15D = 1/q - 2*q^2 - q^5 + 2*q^8 + q^11 + 4*q^14 - 6*q^17 - 2*q^20 + 2*q^23 + ...
%t a[ n_] := SeriesCoefficient[ (QPochhammer[ x] / QPochhammer[ x^5])^2, {x, 0, n}]; (* _Michael Somos_, Aug 26 2015 *)
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A) / eta(x^5 + A))^2, n))}; /* _Michael Somos_, Dec 17 2010 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Nov 27 2000
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