%I A091346
%S A091346 0,1,3,19,135,1171,11823,136459,1771815,25561891,405658143,7022891899,
%T A091346 131714587095,2660335742611,57570797744463,1328913670495339,
%U A091346 32592691757283975,846383665814211331,23200396829832102783
%N A091346 Binomial convolution of A069321(n), where A069321(0)=0, with the sequence 
               of all ones alternating in sign.
%F A091346 a(n)=Sum(C(n, k)(-1)^(n-k)Sum(i!i Stirling2(k, i), i=1, .., k), k=0, 
               .., n). E.g.f.: ((exp(x)-1)/(2-exp(x))^2)*exp(-x)
%F A091346 a(n) = (A000670(n+1)+(-1)^(n+1))/4. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jan 17 2005
%t A091346 Table[Sum[Binomial[n, k](-1)^(n-k)Sum[i!i StirlingS2[k, i], {i, 1, k}], 
               {k, 0, n}], {n, 0, 20}]
%Y A091346 Cf. A083410.
%Y A091346 Sequence in context: A074713 A063395 A074567 this_sequence A035086 A105797 
               A138513
%Y A091346 Adjacent sequences: A091343 A091344 A091345 this_sequence A091347 A091348 
               A091349
%K A091346 easy,nonn
%O A091346 0,3
%A A091346 Mario Catalani (mario.catalani(AT)unito.it), Jan 02 2004