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A062245 Expansion of Hauptmodul for group G'_{27|3}.

%I A062245 #13 Nov 01 2017 09:18:10
%S A062245 1,1,-1,0,0,-1,0,-1,0,-1,-1,1,-1,0,1,1,1,0,2,2,-2,1,1,-2,-1,-2,1,-3,
%T A062245 -3,3,-2,-1,3,2,3,0,5,5,-5,3,1,-5,-3,-5,1,-7,-7,7,-5,-2,7,4,7,-1,11,
%U A062245 11,-11,6,3,-11,-6,-11,2,-15,-15,15,-10,-4,15,9,14,-2,22,22,-22,13,6,-21,-12,-21,4,-30,-30,30,-19,-8,29,17,28,-4,42
%N A062245 Expansion of Hauptmodul for group G'_{27|3}.
%H A062245 J. McKay and A. Sebbar, <a href="http://dx.doi.org/10.1007/s002080000116">Fuchsian groups, automorphic functions and Schwarzians</a>, Math. Ann., 318 (2000), 255-275.
%F A062245 Expansion of q^(1/3) * eta(q^2)^3 * eta(q^9) * eta(q^36) / (eta(q) * eta(q^12) * eta(q^18)^3) in powers of q.
%F A062245 Euler transform of period 36 sequence [ 1, -2, 1, -1, 1, -2, 1, -1, 0, -2, 1, -1, 1, -2, 1, -1, 1, 0, 1, -1, 1, -2, 1, -1, 1, -2, 0, -1, 1, -2, 1, -1, 1, -2, 1, 0, ...].
%F A062245 a(n) = (-1)^n * A062246(n).
%e A062245 G.f. = 1 + x - x^2 - x^5 - x^7 - x^9 - x^10 + x^11 - x^12 + x^14 + x^15 + x^16 + ...
%e A062245 G.f. = 1/q + q^2 - q^5 - q^14 - q^20 - q^26 - q^29 + q^32 - q^35 + q^41 + q^44 + ...
%o A062245 (PARI) {a(n) = local(A); if( n<0, 0,A = x * O(x^n); polcoeff( eta(-x + A) / eta(-x^9 + A), n))}; /* _Michael Somos_, Jun 26 2004 */
%Y A062245 Cf. A007706, A062246.
%K A062245 sign,easy
%O A062245 0,19
%A A062245 _N. J. A. Sloane_, Jul 01 2001