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%I #10 Sep 23 2016 08:14:35
%S 1,1,2,4,8,24,128,624,1920,8448,137472,1203456,835584,-23073792,
%T 1024616448,15237156864,-88263327744,-2230875095040,37715465207808,
%U 842231374479360,-10018210447097856,-278334129792614400,4502327717477744640,131853718231347363840
%N E.g.f. 1/(1-arctan(x)).
%H Vaclav Kotesovec, <a href="/A191700/b191700.txt">Table of n, a(n) for n = 0..440</a>
%F a(n)=n!*sum(k=1..n, (k!*(-1)^((3*n+k)/2)*sum(i=k..n,(2^i*stirling1(i,k)*binomial(n-1,i-1))/i!))/2^k),n>0, a(0)=1.
%t With[{nn=30},CoefficientList[Series[1/(1-ArcTan[x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 05 2013 *)
%t Flatten[{1, Table[n!*Sum[k!*(-1)^((3*n+k)/2)*Sum[2^i*StirlingS1[i, k]*Binomial[n-1, i-1]/i!, {i, k, n}]/2^k, {k, 1, n}], {n, 1, 25}]}] (* _Vaclav Kotesovec_, Sep 23 2016 *)
%o (Maxima)
%o a(n):=n!*sum((k!*(-1)^((3*n+k)/2)*sum((2^i*stirling1(i,k)*binomial(n-1,i-1))/i!,i,k,n))/2^k,k,1,n);
%K sign
%O 0,3
%A _Vladimir Kruchinin_, Jun 12 2011
%E More terms from _Harvey P. Dale_, May 05 2013
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