login
E.g.f. sin(x*tan(x)) (even powers only).
2

%I #19 Sep 24 2019 12:16:21

%S 0,2,8,-24,-4544,-333920,-26272896,-2354853760,-233143441408,

%T -22905309777408,-1339233237800960,428177363623094272,

%U 310125853369485017088,153488683972244927062016,72759436391841580585680896

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

%F 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

%t terms = 15;

%t egf = Sin[x*Tan[x]] + O[x]^(2 terms + 1) ;

%t Partition[CoefficientList[egf, x] * Range[0, 2 terms]!, 2][[All, 1]] (* _Jean-François Alcover_, Sep 24 2019 *)

%o (Maxima)

%o 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 */

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997