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%I #37 Nov 19 2022 21:23:33
%S 1,6,120,840,8064,4224,2196480,199680,5013504,74088448,1568931840,
%T 1899233280,2411724800,2831155200,8757706752,6968215339008,
%U 76890652016640,1488206168064,289223097712640,74371653697536,2197648866017280,10176804748787712,29785769996451840
%N Denominators of the coefficients in a series for the angles in the Spiral of Theodorus.
%C S(i) is the sum of the angles in the first i-1 triangles of the Spiral of Theodorus (in radians). [corrected by _Robert B Fowler_, Oct 23 2022]
%C S(i) = K + sqrt(i) * (2 + 1/(6*i) - 1/(120*i^2) - 1/(840*i^3) + ...) where K is Hlawka's Schneckenkonstante = A105459 * (-1) = -2.1577829966... .
%C The coefficients in the polynomial series are A351861(n)/a(n). The series is asymptotic, but is accurate for even very low values of i.
%C See A351861 for the numerators, as well as references, links, and crossrefs.
%e 2/1 + 1/(6*i) - 1/(120*i^2) - 1/(840*i^3) + ...
%t c[0] = 2; c[n_] := ((2*n - 2)!/(n - 1)!) * Sum[(-1)^(n + 1) * BernoulliB[n - k] * k!/(4^(n - k - 1) * (2*k + 1)! * (n - k)!), {k, 0, n}]; Denominator @ Array[c, 30, 0] (* _Amiram Eldar_, Feb 22 2022 *)
%Y Cf. A351861 (numerators).
%K nonn,frac,easy
%O 0,2
%A _Robert B Fowler_, Feb 22 2022