A012021 Expansion of e.g.f.: tan(sin(arctan(x))) (odd powers only).

1, -1, 1, 167, -14303, 1383887, -170123615, 26560717367, -5162935778879, 1219537456849055, -340794504958201919, 109077799391707298759, -38112045733323708444959, 13139859774638771226676847

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = (2*n-1)!*sum(m=1..n, (sum(j=1..2*m-1, j!*2^(2*m-j-1)*(-1)^(n+j)*Stirling2(2*m-1,j)))*binomial((2*n-3)/2,(n-m))/(2*m-1)!), n>0. - Vladimir Kruchinin, May 19 2011

Example

tan(sin(arctan(x))) = x - (1/3!)*x^3 + (1/5!)*x^5 + (167/7!)*x^7 - (14303/9!)*x^9 + ...

Mathematica

nn = 20; Table[(CoefficientList[Series[Tan[x/Sqrt[1 + x^2]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 03 2015 *)

Prog

(Maxima)
a(n):=(2*n-1)!*sum((sum(j!*2^(2*m-j-1)*(-1)^(n+j)*stirling2(2*m-1, j), j, 1, 2*m-1))*binomial((2*n-3)/2, (n-m))/(2*m-1)!, m, 1, n); /* Vladimir Kruchinin, May 19 2011 */

Crossrefs

Sequence in context: A201853 A142843 A290757 * A175558 A289743 A308280

Adjacent sequences: A012018 A012019 A012020 * A012022 A012023 A012024

Keyword

sign

Author

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

Status

approved