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%I #17 Jan 18 2013 08:29:20
%S 1,2,32,768,49152,1,56623104,3170893824,541165879296,175337744891904,
%T 28054039182704640,29389945810452480,2844006276185865584640,
%U 147888326361665010401280,25765432859454526256578560,83480002464632665071314534400
%N Denominator of series coefficients for Archimedes' spiral which transforms into Galileo's spiral.
%C Numerators are listed in A202407 which is the main entry for these sequences.
%t km = 16; a[0] = 0; r[t_] = Sum[a[k] t^(2 k), {k, 0, km}]; coes = CoefficientList[Series[r'[t]^2 + r[t]^2 - t^2 , {t, 0, 2 km}], t] // Union // Rest; Table[a[k], {k, 0, km}] /. Solve[Thread[coes == 0] ] // Last // Most // Denominator (* _Jean-François Alcover_, Jan 18 2013 *)
%K nonn,frac
%O 0,2
%A _Mikhail Gaichenkov_, Dec 19 2011
%E Corrected and extended by _Max Alekseyev_, Dec 19 2011
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