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%I #16 Jul 02 2022 16:09:02
%S 1,3,45,945,14175,93555,638512875,273648375,44405668125,
%T 194896477400625,32157918771103125,201717854109646875,
%U 3028793579456347828125,698952364489926421875,80664808595725181953125,5660878804669082674070015625
%N Denominators of coefficients in expansion of x/((x^2+1)*arctan(x)), even powers only.
%C The numerators are given in A216254.
%C Terms up to n=13 are identical to A154289; this is just a coincidence.
%H G. C. Greubel, <a href="/A225149/b225149.txt">Table of n, a(n) for n = 0..249</a>
%F a(n) = denominator((-1)^n * Sum_{m=0..2*n} 2^m * (Sum_{k=0..m} k! * Stirling2(m,k) * Stirling1(m+k,m) / (m+k)!) * binomial(2*n,m)).
%t Denominator[With[{nn = 50}, Table[(CoefficientList[Series[x/((x^2 + 1)*ArcTan[x]), {x, 0, 2*nn}], x])[[n]], {n, 1, 2*nn + 1, 2}]]] (* _G. C. Greubel_, Apr 12 2017 *)
%o (PARI) x='x+O('x^66); v=Vec(x/((x^2+1)*atan(x))); vector(#v\2, n, denominator(v[2*n-1])) \\ _Joerg Arndt_, Apr 30 2013
%o (PARI) a(n) = denominator((-1)^n*sum(l=0,2*n, 2^l * (sum(k=0,l, (k!*stirling(l,k,2) * stirling(l+k,l,1)) / (l+k)!)) * binomial(2*n,l))); \\ _Michel Marcus_, Apr 30 2013
%K nonn,frac
%O 0,2
%A _Michel Marcus_, Apr 30 2013
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