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%I #27 Nov 01 2021 11:43:48
%S 0,1,-1,3,-10,41,-232,1467,-11408,100625,-1000704,11103155,-135118080,
%T 1795927225,-25845415936,400540116971,-6651228620800,117802787966241,
%U -2216949901393920,44174901566136419,-929133071750004736
%N Expansion of e.g.f. log(1 + tan(sin(x))).
%t With[{nn=20},CoefficientList[Series[Log[1+Tan[Sin[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 01 2021 *)
%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*(-1)^(m-1),m,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%o (PARI)
%o x='x+O('x^66); /* that many terms */
%o egf=log(1+tan(sin(x))); /* = 0 + x - 1/2*x^2 + 1/2*x^3 - 5/12*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
%E Previous Mathematica program replaced by _Harvey P. Dale_, Nov 01 2021
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