%I #12 Jan 29 2018 02:53:45
%S 1,0,2,-3,12,-70,418,-2604,20048,-189288,1883592,-19386840,226594632,
%T -3022978608,42088762896,-602721577080,9458674967808,-163559679584064,
%U 2928052794471360,-53694788632038144
%N Expansion of e.g.f. exp(arctan(x)*log(x+1)).
%F a(n) = n!*sum(k=1..n, 2^(-k)*k!* sum(j=0..n/2-k, ((sum(i=0..2*j, (2^(i+k)*Stirling1(i+k,k)*binomial(2*j+k-1,i+k-1))/(i+k)!))*(-1)^j*Stirling1(n-2*j-k,k))/(n-2*j-k)!)), n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 01 2011
%e exp(arctan(x)*log(x+1)) = 1 + (2/2!)*x^2 - (3/3!)*x^3 + (12/4!)*x^4 - (70/5!)*x^5 + ...
%o (Maxima)
%o a(n):=n!*sum(2^(-k)*k!*sum(((sum((2^(i+k)*stirling1(i+k,k)*binomial(2*j+k-1,i+k-1))/(i+k)!,i,0,2*j))*(-1)^j*stirling1(n-2*j-k,k))/(n-2*j-k)!,j,0,n/2-k),k,1,n); /* _Vladimir Kruchinin_, Jun 01 2011 */
%K sign
%O 0,3
%A Patrick Demichel (patrick.demichel(AT)hp.com)