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%I #31 Sep 06 2018 18:34:51
%S 1,0,2,1,2,3,4,5,7,8,11,13,16,19,25,28,35,41,50,58,71,81,98,113,134,
%T 154,183,208,244,280,326,371,431,489,565,641,735,832,953,1075,1225,
%U 1382,1569,1764,1999,2243,2533,2839,3195,3575,4018,4484,5026,5604,6267
%N Coefficients of replicable function number 49a.
%H G. C. Greubel, <a href="/A058700/b058700.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 a(n) ~ exp(4*Pi*sqrt(n)/7) / (sqrt(14)*n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017
%F Expansion of A - 3*q, where A = (eta(q^7)^4 + 7*eta(q)^2*eta(q^49)^2)/ (eta(q)*eta(q^49)*(eta(q)^2 + 7*eta(q)*eta(q^49) + 7*eta(q^49)^2)), in powers of q. - _G. C. Greubel_, Jun 17 2018
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (49 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, Sep 06 2018
%e T49a = 1/q + 2*q + q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 7*q^7 + 8*q^8 + ...
%t QP = QPochhammer; A1 = QP[q]; A2 = QP[q^7]; A3 = QP[q^49]; s = -3 q + (A2^4 + 7*q^3*A1^2*A3^2)/(A1*A3)/(A1^2 + 7*q^2*A1*A3 + 7*q^4*A3^2) + O[q]^30; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 16 2015, adapted from A136560 *)
%t a[ n_] := With[ {e1 = QPochhammer[ q], e2 = QPochhammer[ q^7], e3 = QPochhammer[ q^49]}, SeriesCoefficient[ -3 + (e2^4 + 7 q^3 e1^2 e3^2) / (q e1 e3 (e1^2 + 7 q^2 e1 e3 + 7 q^4 e3^2)), {q, 0, n}]]; (* _Michael Somos_, Sep 06 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^7)^4 + 7*q^3*(eta(q)*eta(q^49))^2)/( eta(q)*eta(q^49)*(eta(q)^2 + 7*q^2*eta(q)*eta(q^49) + 7*q^4* eta(q^49)^2)); Vec(A-3*q) \\ _G. C. Greubel_, Jun 17 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Vincenzo Librandi_, Nov 16 2015
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