A012022 Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only).

1, -5, 129, -7965, 903105, -163451925, 43259364225, -15764670046125, 7571150452490625, -4634731528895593125, 3522824632122301130625, -3255279003622294051528125, 3593928024032353882700450625

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n) = (2*n+1)!*(-1)^n*Sum_{j=1..n+1} binomial((2*n-1)/2, n+1-j) /(2*j-1). - Vladimir Kruchinin, May 19 2011

E.g.f.: Sum_{n >= 0} a(n)*x^(2n+1)/(2n+1)! = arctan(sin(arctan(x))).

a(n) = (2*n+1)! * [x^(2*n+1)] arctan(sin(arctan(x))).

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcTan[Sin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Dec 11 2013 *)

Prog

(Maxima)
a(n):= ((2*n+1)!* (-1)^n *sum(binomial((2*n-1)/2, n+1-j)/(2*j-1), j, 1, n+1)); /* Vladimir Kruchinin, May 19 2011 */

Crossrefs

Sequence in context: A094074 A012218 A012136 * A012176 A012187 A012083

Adjacent sequences: A012019 A012020 A012021 * A012023 A012024 A012025

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved