This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A223068 #16 Jan 05 2017 17:15:06
%S A223068 1,16,3072,737280,1321205760,951268147200,2009078326886400,
%T A223068 265928913086054400,44931349155019751424000,
%U A223068 109991942731488351485952000,668751011807449177034588160000,2471703739640332158319837839360000
%N A223068 A sequence related to the period T of a simple gravity pendulum for arbitrary amplitudes.
%C A223068 The period T of a simple gravity pendulum for arbitrary amplitudes is given by a complicated formula, see A223067. The Taylor series expansion of T as a function of the angular displacement phi leads for the denominators of the even powers of phi to the sequence given above and for the numerators to A223067.
%e A223068 T = 2*Pi*sqrt(L/g) * (1 + (1/16)*phi^2 + (11/3072)*phi^4 + (173/737280)*phi^6 + ... ).
%p A223068 nmax:=11: f := series(1/((Pi/4)*(1+cos(phi/2))/EllipticK((1-cos(phi/2))/(1+cos(phi/2)))), phi, 2*nmax+1): for n from 0 to nmax do a(n):= denom(coeff(f, phi, 2*n)) od: seq(a(n), n=0..nmax); # _Johannes W. Meijer_, Jan 05 2017
%t A223068 s = Series[EllipticK[Sin[t/2]^2 ], {t, 0, 50}]; CoefficientList[2*s, t^2] // Denominator (* _Jean-François Alcover_, Oct 07 2014 *)
%Y A223068 Cf. A223067 (numerators), A019692 (2*Pi).
%Y A223068 Cf. A280442, A280443.
%K A223068 nonn,easy,frac
%O A223068 0,2
%A A223068 _Johannes W. Meijer_, Mar 14 2013