A202408 Denominator of series coefficients for Archimedes' spiral which transforms into Galileo's spiral.

1, 2, 32, 768, 49152, 1, 56623104, 3170893824, 541165879296, 175337744891904, 28054039182704640, 29389945810452480, 2844006276185865584640, 147888326361665010401280, 25765432859454526256578560, 83480002464632665071314534400

Offset: 0

Author

Mikhail Gaichenkov, Dec 19 2011

Keywords

• nonn
• frac

Comments

Numerators are listed in A202407 which is the main entry for these sequences.

Programs

Mathematica

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 *)

Extensions

Corrected and extended by Max Alekseyev, Dec 19 2011