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%I #36 Mar 12 2021 22:24:42
%S 1,0,6,-8,17,-32,54,-80,116,-192,290,-408,585,-832,1192,-1648,2237,
%T -3072,4156,-5576,7414,-9824,12964,-16896,22002,-28544,36794,-47184,
%U 60185,-76736,97388,-122864,154615,-194048,242904,-302800,376271,-466720,577176,-711840
%N McKay-Thompson series of class 10B for the Monster group with a(0) = 0.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A058098/b058098.txt">Table of n, a(n) for n = -1..5000</a> (terms -1..997 from G. A. Edgar)
%H D. Ford, J. McKay and S. P. Norton, <a href="https://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 Expansion of q^-1 * (chi(-q) * chi(-q^5))^4 + 4 in powers of q where chi() is a Ramanujan theta function.
%F Expansion of (eta(q) * eta(q^5) / (eta(q^2) * eta(q^10)))^4 + 4 in powers of q.
%F G.f.: (Product_{k>0} (1 + x^k) * (1 + x^(5*k)))^-4 + 4.
%F a(n) = A132040(n) unless n = 0. a(n) = -(-1)^n * A112158(n). - _Michael Somos_, Feb 02 2012
%F a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017
%e T10B = 1/q + 6*q - 8*q^2 + 17*q^3 - 32*q^4 + 54*q^5 - 80*q^6 + ...
%t QP = QPochhammer; s = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 13 2015, adapted from PARI *)
%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, n))} /* _Michael Somos_, Feb 02 2012 */
%Y Cf. A000521, A007240, A007241, A007267, A014708, A045478.
%Y Cf. A112158, A132040.
%K sign
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
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