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%I #18 Mar 12 2021 22:24:43
%S 1,1,-1,1,2,-1,-2,-1,3,0,-4,1,5,1,-7,0,8,0,-10,-1,13,-2,-16,0,20,3,
%T -24,2,30,-2,-36,-4,43,0,-52,3,61,2,-73,1,86,-1,-102,-3,120,-4,-140,1,
%U 165,8,-192,5,224,-6,-260,-10,301,-2,-348,7,401,7,-462,2,530,-2,-608,-8,696,-10,-796,3,909,18,-1035,12
%N McKay-Thompson series of class 24h for the Monster group.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A112165/b112165.txt">Table of n, a(n) for n = 0..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 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Convolution square is A187197. - _Michael Somos_, Aug 31 2014
%F Expansion of chi(-x^4)^2 * chi(-x^12)^2 / (chi(-x^2) * chi(-x^6)) in powers of x where chi() is a Ramanujan theta function. - _Michael Somos_, Apr 22 2015
%F a(n) = A255391(2*n - 1) = A255396(2*n - 1). - _Michael Somos_, Apr 22 2015
%e G.f. = 1 + x - x^2 + x^3 + 2*x^4 - x^5 - 2*x^6 - x^7 + 3*x^8 - 4*x^10 + ...
%e T24h = 1/q + q - q^3 + q^5 + 2*q^7 - q^9 - 2*q^11 - q^13 + 3*q^15 + ...
%t a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2] QPochhammer[ x^6])^3 / (QPochhammer[ x] QPochhammer[ x^3] QPochhammer[ x^4]^2 QPochhammer[ x^12]^2), {x, 0, n}]; (* _Michael Somos_, Aug 31 2014 *)
%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^3 * eta(x^6 + A)^3 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A)^2 * eta(x^12 + A)^2), n))}; /* _Michael Somos_, Aug 31 2014 */
%Y Cf. A187197, A255391, A255396.
%K sign
%O 0,5
%A _Michael Somos_, Aug 28 2005
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