A191300 - OEIS

%I #11 Jan 15 2018 15:33:19

%S 1,1,1,4,-62,3600,-312784,39782976,-6974450160,1614143578368,

%T -477069128688384,175403422124098560,-78541482962813397504,

%U 42088662436010509209600,-26598972441544647820185600,19578612638548987656917630976

%N Expansion of exp(x*arctan(x)) = 1 + Sum_{n>0} a(n)*x^(2*n)/(2*n-1)!.

%F a(n)=(2*n-1)!*sum(k=1..n, ((-1)^(n-k)*sum(i=0..2*n, (2^i*stirling1(i+k,k)*binomial(2*n-k-1,i+k-1))/(i+k)!))), n>0, a(0)=1.

%o (Maxima)

%o a(n):=(2*n-1)!*sum(((-1)^(n-k)*sum((2^i*stirling1(i+k,k)*binomial(2*n-k-1,i+k-1))/(i+k)!,i,0,2*n)),k,1,n);

%K sign

%O 0,4

%A _Vladimir Kruchinin_, May 30 2011