Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #27 Jan 27 2018 06:30:28
%S 1,1,1,2,5,8,13,-64,-855,-5632,-38791,-205184,-747539,-240640,
%T 59637061,859820032,9421489105,90170851328,573991066225,1502445600768,
%U -49290541346219,-1320541298393088,-20481513828195331,-272882319216148480
%N Expansion of e.g.f. exp(tan(sin(x))).
%F a(n) = Sum(m=1..n, Sum(k=m..n, (((-1)^(k-m)+1)*(Sum(j=m..k, C(j-1,m-1)*j! *2^(k-j-1) *Stirling2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)*Sum(i=0..k/2, (2*i-k)^n *C(k,i)*(-1)^((n+k)/2-i)))/(2^k*k!))/m!). - _Vladimir Kruchinin_, May 05 2011
%t With[{nn=30},CoefficientList[Series[Exp[Tan[Sin[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 25 2011 *)
%o (Maxima)
%o a(n):=sum(sum((((-1)^(k-m)+1)*(sum(binomial(j-1,m-1)*j!*2^(k-j-1) *stirling2(k,j)*(-1)^((m+k)/2+j),j,m,k))*((-1)^(n-k)+1)*sum((2*i-k)^n *binomial(k,i)*(-1)^((n+k)/2-i),i,0,k/2))/(2^k*k!),k,m,n)/m!,m,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%o (PARI)
%o x='x+O('x^66); /* that many terms */
%o egf=exp(tan(sin(x))); /* = 1 + x + 1/2*x^2 + 1/3*x^3 + 5/24*x^4 + ... */
%o Vec(serlaplace(egf)) /* show terms */ /* _Joerg Arndt_, May 05 2011 */
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
%E Definition corrected by _Joerg Arndt_, May 05 2011