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 A225149 Denominators of coefficients in expansion of x/((x^2+1)*arctan(x)), even powers only. 2
 1, 3, 45, 945, 14175, 93555, 638512875, 273648375, 44405668125, 194896477400625, 32157918771103125, 201717854109646875, 3028793579456347828125, 698952364489926421875, 80664808595725181953125, 5660878804669082674070015625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The numerators are given in A216254. Terms up to n=13 are identical to A154289, this is just a coincidence. LINKS G. C. Greubel, Table of n, a(n) for n = 0..249 FORMULA a(n) = denominator((-1)^n*sum(l=0..2*n, 2^l * (sum(k=0..l, (k!*stirling2(l,k) * stirling1(l+k,l)) / (l+k)!)) * binomial(2*n,l))). MATHEMATICA 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 *) PROG (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 (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 CROSSREFS Sequence in context: A202437 A008931 A036278 * A154289 A171080 A188681 Adjacent sequences:  A225146 A225147 A225148 * A225150 A225151 A225152 KEYWORD nonn,frac AUTHOR Michel Marcus, Apr 30 2013 STATUS approved

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Last modified May 16 05:06 EDT 2022. Contains 353690 sequences. (Running on oeis4.)