A225149 Denominators of coefficients in expansion of x/((x^2+1)*arctan(x)), even powers only.

1, 3, 45, 945, 14175, 93555, 638512875, 273648375, 44405668125, 194896477400625, 32157918771103125, 201717854109646875, 3028793579456347828125, 698952364489926421875, 80664808595725181953125, 5660878804669082674070015625

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_{m=0..2*n} 2^m * (Sum_{k=0..m} k! * Stirling2(m,k) * Stirling1(m+k,m) / (m+k)!) * binomial(2*n,m)).

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