%I #28 Jun 17 2018 22:05:33
%S 1,2,17,46,116,252,533,1034,1961,3540,6253,10654,17897,29284,47265,
%T 74868,117158,180608,275562,415300,620210,916860,1344251,1953974,
%U 2819664,4038300,5746031,8122072,11413112,15943576,22153909,30620666
%N McKay-Thompson series of class 11A for the Monster group with a(0) = 2.
%H G. C. Greubel, <a href="/A134784/b134784.txt">Table of n, a(n) for n = -1..1000</a>
%H M. Koike, <a href="http://projecteuclid.org/euclid.nmj/1118787871">Mathieu group M24 and modular forms</a>, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Associated with permutations in Mathieu group M24 of shape (11)^2(1)^2.
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t).
%F a(n) ~ exp(4*Pi*sqrt(n/11)) / (sqrt(2)*11^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017
%F Expansion of -4 + (1 + 3*F)^2* (1/F + 1 + 3*F) where F = eta(q^3)* eta(q^33)/ (eta(q)* eta(q^11)) in powers of q. - _G. C. Greubel_, Jun 17 2018
%F Expansion of 3 + (1 + A)*(16 + A^2)/A^2, where A = (eta(q)*eta(q^11)/ (eta(q^2)*eta(q^22)))^2, in powers of q. - _G. C. Greubel_, Jun 17 2018
%e G.f. = 1/q + 2 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...
%t QP = QPochhammer; F = q*QP[q^3]*(QP[q^33]/(QP[q]*QP[q^11])); s = q*(-4 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 16 2015, adapted from A058205 *)
%o (PARI) {a(n) = my(A); if( n<-1, 0, A = x^2 * O(x^n); A = (eta(x + A) * eta(x^11 + A) / ( eta(x^2 + A) * eta(x^22 + A) ))^2 / x; polcoeff( 3 + (1 + A) * (1 + 16 / A^2), n))};
%Y A058205(n) = a(n) unless n=0. Convolution with A006571 is A028996.
%Y Cf. A128525, A003295. [From _R. J. Mathar_, Dec 13 2008]
%K nonn
%O -1,2
%A _Michael Somos_, Nov 22 2007
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