A009516 - OEIS

%I #13 Apr 01 2017 22:33:33

%S 1,4,12,-1472,-159792,-16362304,-1834702400,-218477736448,

%T -23399883425536,-225490426670080,1498513205985651712,

%U 985137918553296764928,536781621147089121005568,285950922368074600238661632

%N Expansion of sin(tan(x)/cos(x)).

%t Sin[ Tan[ x ]/Cos[ x ] ] (* Odd Part *)

%o (Maxima)

%o a(n):=4*sum(((-1)^(m)*sum((binomial(m+k-1,2*m)*sum((2*i-2*k+1)^(2*n+1)*binomial(2*k-1,i)*(-1)^(i-n+k),i,0,k-1/2))/2^(2*k),k,m+1,n+1))/(2*m+1)!,m,0,n); /* _Vladimir Kruchinin_, Jun 23 2011 */

%K sign

%O 0,2

%A _R. H. Hardin_

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