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%I #21 Jan 27 2018 06:29:00
%S 1,1,1,4,13,56,301,1688,11705,84160,698521,6141312,59340997,613282944,
%T 6782462597,80158806016,1000434618609,13267800137728,184576848771889,
%U 2710082835353600,41577074746699261,669033814167273472
%N Expansion of exp(x/cos(x)).
%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F a(n) = sum(binomial(n,k)*(if n=k then 1 else if oddp(n-k) then 0 else sum(sum(binomial(m,j)*2^(1-j)*sum((-1)^((n-k)/2)*binomial(j,i)*(j-2*i)^(n-k),i,0,floor((j-1)/2))*(-1)^(m-j),j,1,m)*(-1)^m*binomial(k+m-1,k-1),m,1,n-k)),k,1,n), n>0. - _Vladimir Kruchinin_, Sep 12 2010
%t With[{nn=30},CoefficientList[Series[Exp[x/Cos[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 10 2015 *)
%o (Maxima) a(n):=sum(binomial(n,k)*(if n=k then 1 else if oddp(n-k) then 0 else sum(sum(binomial(m,j)*2^(1-j)*sum((-1)^((n-k)/2)*binomial(j,i)*(j-2*i)^(n-k),i,0,floor((j-1)/2))*(-1)^(m-j),j,1,m)*(-1)^m*binomial(k+m-1,k-1),m,1,n-k)),k,1,n); /* _Vladimir Kruchinin_, Sep 12 2010 */
%K nonn,easy
%O 0,4
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
%E Prior Mathematica program replaced by _Harvey P. Dale_, Jul 10 2015