A009515 E.g.f. sin(x*tan(x)) (even powers only).

0, 2, 8, -24, -4544, -333920, -26272896, -2354853760, -233143441408, -22905309777408, -1339233237800960, 428177363623094272, 310125853369485017088, 153488683972244927062016, 72759436391841580585680896

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Programs

Mathematica

terms = 15;
egf = Sin[x*Tan[x]] + O[x]^(2 terms + 1) ;
Partition[CoefficientList[egf, x] * Range[0, 2 terms]!, 2][[All, 1]] (* Jean-François Alcover, Sep 24 2019 *)

Maxima

a(n):=(sum(binomial(2*n,2*m+1)*(sum(binomial(j-1,2*m)*j!*(-1)^(n+m+j)*2^(2*n-2*m-j-1)*stirling2(2*n-2*m-1,j),j,2*m+1,2*n-2*m-1)),m,0,n-1/2)); /* Vladimir Kruchinin, Jun 23 2011 */

Formula

a(n)=(sum(m=0..n-1/2, binomial(2*n,2*m+1)*(sum(j=2*m+1..2*n-2*m-1, binomial(j-1,2*m)*j!*(-1)^(n+m+j)*2^(2*n-2*m-j-1)*stirling2(2*n-2*m-1,j))))). - Vladimir Kruchinin, Jun 23 2011

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997