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%I #25 Oct 30 2022 03:45:41
%S 1,1,1,2,5,8,13,-232,-2199,-25600,-218311,-2258048,-20057555,
%T -212565376,-1933691003,-21159275264,-181405779887,-1935285600256,
%U -10159446470927,-49976214294528,2835996855537109,63805712413261824
%N Expansion of exp(sin(tan(x))).
%H Vladimir Kruchinin and 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(sum(if oddp(n+k) or oddp(k-m) then 0 else (-1)^((n+k)/2)*sum(j!*stirling2(n,j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1,k-1),j,k,n)*2^(1-m)*sum((-1)^(floor((k+m)/2)-i)*binomial(m,i)*(2*i-m)^k/k!/m!,i,0,floor(m/2)) ,k,m,n),m,1,n), n>0. - _Vladimir Kruchinin_, Sep 01 2010
%t With[{nn=30},CoefficientList[Series[Exp[Sin[Tan[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 13 2018 *)
%o (Maxima) a(n):=sum(sum(if oddp(n+k) or oddp(k-m) then 0 else (-1)^((n+k)/2)*sum(j!*stirling2(n,j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1,k-1),j,k,n)*2^(1-m)*sum((-1)^(floor((k+m)/2)-i)*binomial(m,i)*(2*i-m)^k/k!/m!,i,0,floor(m/2)) ,k,m,n),m,1,n); /* _Vladimir Kruchinin_, Sep 01 2010 */
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Prior Mathematica program replaced by _Harvey P. Dale_, Oct 13 2018
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