A003705 E.g.f. tan(sin(x)) (odd powers only).

1, 1, -3, -107, -1095, 41897, 3027637, 34528445, -11832720271, -1190157296815, 22592230600813, 23107531656941541, 2633888933338158633, -362759000929143575815, -189312598480126813670107, -18315162183020706728157939

Offset: 0

Author

R. H. Hardin, Simon Plouffe

Keywords

• sign

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

Programs

Mathematica

With[{nn = 50}, Take[CoefficientList[Series[Tan[Sin[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *)

Maxima

a(n):=2*sum(((sum(j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1,j),j,1,2*m+1))*sum((2*i-(2*m+1))^(2*n-1)*binomial(2*m+1,i)*(-1)^(n-i),i,0,(2*m+1)/2))/(2*m+1)!,m,0,n-1); /* Vladimir Kruchinin, Jun 11 2011 */

Formula

a(n) = 2*sum(m=0..n-1, ((sum(j=1..2*m+1, j!*2^(-j)*(-1)^(j+1)*stirling2(2*m+1,j)))*sum(i=0..(2*m+1)/2, (2*i-(2*m+1))^(2*n-1)*binomial(2*m+1,i)*(-1)^(n-i)))/(2*m+1)!). [Vladimir Kruchinin, Jun 11 2011]

Extensions

Changed offset from 1 to 0 by Vincenzo Librandi, Apr 11 2014