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

0,2

Comments

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

Links

Table of n, a(n) for n=0..15.

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 *)

Crossrefs

Sequence in context: A198599 A009517 A354382 * A069182 A333772 A012233

Adjacent sequences: A202405 A202406 A202407 * A202409 A202410 A202411

Keyword

nonn,frac

Author

Mikhail Gaichenkov, Dec 19 2011

Extensions

Corrected and extended by Max Alekseyev, Dec 19 2011

Status

approved